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By using the most generalized gamma function (parametric gamma function, or p-gamma function), we present the most generalized Rabotnov function, called the p-Rabotnov function. Consequently, new fractal–fractional differential and integral operators of a complex variable in an open unit disk are defined and investigated analytically and geometrically. We address some inequalities involving the generalized fractal–fractional integral operator in some spaces of analytic functions. A novel complex fractal–fractional integral transform (CFFIT) is presented. A normalization of the proposed CFFIT is observed in the open unit disk. Examples are illustrated for power series of analytic functions. [ABSTRACT FROM AUTHOR]

In order to examine various geometric features, we expanded the supertrigonometric function (STF) and superhyperbolic function (SHF) into the open unit disk. A convolution differential operator of the STF provides the formulas. The suggested operator works with both integral and double differential inequalities. As a result, we present a collection of findings that includes recent works. The idea of subordination and superordination serves as a guide for our method, and we then developed the primary conclusion as a double side’s theorem. [ABSTRACT FROM AUTHOR]

Signcryption is a highly efficient approach to simultaneously achieving message confidentiality and authentication in Human-Centered IoT (HC-IoT) systems. HCIoT is a new field of study that links various aspects of life such as smart cards, business, e-commerce, healthcare, and sensitive private data. A number of intelligent systems favor human intervention to start automated tasks. A number of smart devices have a social effect in that they should be capable of changing their functional model based on the behavior of different humans. It has boosted the development of information exchange over the IoT and enabled networks. It encompasses cellular, vehicular, and human healthcare by utilizing middleware. Currently, group signcryption schemes are gaining widespread popularity in HC-IoT environments. HC-IoT is useful in electronic cash systems, lightweight devices, multi-server networks, and more. However, most signcryption schemes use bilinear pairing that is computationally intensive, and there is a need for more efficient signcryption schemes. In order to solve this issue, this paper introduces an efficient Certificateless Group-oriented Signcryption (CGS) scheme using Quantum Chebyshev Chaotic Maps (QCCM) without employing bilinear pairing. The proposed QCCM-CGS scheme's standout feature is that any group signcrypter can signcrypt a text/information with the group manager (GM) and then present it to the verifier for verification. By using the public conditions of the group, the verifier approves the validity of the signcrypted text and cannot connect the signcrypted text to the conforming signcrypter. However, a legitimate signcrypted text cannot be generated even by the GM or any signcrypter of that group unaccompanied. In situations where there is a legal disagreement, such as non-repudiation of the signature, the GM can reveal the identity of the signcrypter. The presented scheme is adequately secured from the indistinguishably chosen ciphertext attack. The computationally challenging problem, QCCM, is used as the foundation for the construction of traceability, unforgeability, unlinkability, and security. Lastly, the security review of the projected scheme clearly shows significant consistency, and it can be easily deployed in vulnerable security applications. [ABSTRACT FROM AUTHOR]

It is well known that there are two important classes of analytic functions of Ma-Minda type (MMT): Ma-Minda starlike and Ma-Minda convex functions. In this work, we suggest a new class of analytic functions, which is normalized in the open unit disk. The suggested class is generated by a roulette curve formula, which satisfies the symmetric behavior in the open unit disk. A roulette curve is shaped as the path outlined by the sum of two complex numbers, each affecting at a uniform rapidity in a circle. Special cases are illustrated involving special functions. Graphics of the curve are illustrated by using Mathematica 13.3. [ABSTRACT FROM AUTHOR]

Non-local operators of differentiation are bestowed with capabilities of encompassing complex natural into mathematical equations. Symmetry as invariance under a specified group of transformations can allow for the concept to be applied extensively not only to spatial figures but also to abstract objects like mathematical expressions which can be said to be expressions of physical relevance, in particular dynamical equations. Derived from this point of view, it can be noted that the more complex physical problems are, the more complex mathematical operators of differentiation are required. Accordingly, the fractal–fractional operators (FFOs) are expanded into the complex plane in our research which revolves around a unique class of normalized analytic functions in the open unit disk. To bring FFOs (differential and integral) into the normalized class, the study aims to expand and modify them along with the investigation of the FFOs geometrically. The qualities of convexity and starlikeness are implicated in this study where the differential subordination technique serves as the foundation for the inquiry under consideration. Furthermore, a collection of differential FFO inequalities is taken into account, demonstrating that the normalized Fox–Wright function can contain all FFOs. Besides these steps, the concept of Grunsky factors is applied to investigate symmetry, while boundary value issues involving FFOs are probed. Consequently, the related properties and applications can be further developed, which requires the devotion to differential fractional problems and diverse complex problems in relation to viable applications, pointing out the room to modify and upgrade the existing methods for more optimal outcomes in challenging real-world problems. [ABSTRACT FROM AUTHOR]

The k -convoluted operators related to the k -Whittaker function, confluent hypergeometric function of the first kind, have been developed using the k -symbol calculus in which this sort of calculus presents a generalization of the gamma function. K -symbol fractional calculus is employed to generalize and extend many differential and integral operators of fractional calculus. Based on this premise, a new geometric formula for normalized functions in the symmetric domain known as the open unit disk using the conformable fractional differential operator has been presented in this study. Thus, our technique entails investigating the most well-known geometric properties of this new operator, such as the subordination features and coefficient bounds so that the theory of differential subordination can be adjusted accordingly. By means of this technique, numerical results have been investigated for the proposed method. To this end, a few prominent corollaries of our primary findings as standout instances have been pointed out based on the positivity of the solutions, computational and numerical analyses. [ABSTRACT FROM AUTHOR]

Convolution operators have profited in various areas of science. They are utilized in the investigations of computing techniques. A new convolution operator linked to a specific class of multi-valent meromorphic functions in the punctured unit disk (symmetric domain) is formulated. This analysis uncovers certain properties on the connections as well as the power series. We study a novel class of holomorphic functions concerning the recommended new operator. The second part of the outcome concerns the boundedness of the suggested difference structure given by the proposed operator. We focus on the Bloch space of meromorphic functions in the open unit disk. In this case, we use the spherical derivative. To obtain the maximum value of the polar derivative of the polynomials created by their partial sums, we use their partial sums as applications of the suggested operator. [ABSTRACT FROM AUTHOR]

In this investigation, we suggest different systems: the k-symbol fractional Lozi system (FLS), the k-symbol fractional Lozi system. We examine several of these systems' crucial dynamics. Moreover, we explore the sufficient and necessary conditions for the k-symbol fractional dynamic systems to be stable and asymptotically stable. Consequently, we provide the sufficient conditions on the k-symbol FLS to attain a steady and asymptotically steady zero resolutions. Additionally, we suggest in control laws designed to stabilize a combination of these systems. In this study, we assume 1D-controller and 2D-controller systems. [ABSTRACT FROM AUTHOR]

A complex Layla and Majnun model system (CLMMS) is suggested in this study for a complex variable in the open-unit disk. Analytic solutions are discovered by using a technique of bounded turning functions. The set of necessary conditions is illustrated involving some special cases. [ABSTRACT FROM AUTHOR]

An intelligent access web selection must have an illustration of the favorites for making decisions. For this, we will use the theory of a utility function describing which situations are better for the costumers. Obviously, such utility is qualified and achieved all properties. We propose new single-pattern and multi-pattern utility procedures to best capture the user agreement and sensitivity facing up to a package of access web features. Mathematical propositions and numerical analysis slow down the ability and the practicality of our proposed simulations. For this purpose, we utilize a new methodology which is based on the concept of fractional entropy. This concept has a dominant effect on information theory. [ABSTRACT FROM AUTHOR]

Images are frequently disrupted by noise of all kinds, making image restoration very challenging. There have been many different image denoising models proposed over the last few decades. Some models preserve the image's smooth region, while others preserve the texture margin. One of these methods is by using quantum calculus. Quantum calculus is a branch of mathematics that deals with the manipulation of functions and operators in a quantum mechanical setting. It has been used in image processing to improve the speed and accuracy of image-processing algorithms. In quantum computing, entropy can be defined as a measure of the disorder or randomness of a quantum state. The concept of local fractional entropy has been used to study a wide range of quantum systems. In this study, an image denoising model is proposed based on the quantum calculus of local fractional entropy (QC-LFE) to remove a Gaussian noise. The local fractional entropy is used to estimate the image pixel probability, while the quantum calculus is used to estimate the convolution window mask for image denoising. A processing fractional mask with n x n elements was used in the suggested denoising algorithm. The proposed image denoising algorithm uses mask convolution to process each corrupted pixel one at a time. The proposed denoising algorithm's effectiveness is assessed using peak signal-to-noise ratio and visual perception (PSNR). The experimental findings show that, compared to other similar fractional operators, the proposed method can better preserve texture details when denoising. [ABSTRACT FROM AUTHOR]

The symmetric Schur process has many different types of formals, such as the functional differential, functional integral, and special functional processes based on special functions. In this effort, the normalized symmetric Schur process (NSSP) is defined and then used to determine the geometric and symmetric interpretations of mathematical expressions in a complex symmetric domain (the open unit disk). To obtain more symmetric properties involving NSSP, we consider a symmetric differential operator. The outcome is a symmetric convoluted operator. Geometrically, studies are presented for the suggested operator. Our method is based on the theory of differential subordination. [ABSTRACT FROM AUTHOR]

The notion of k-symbol special functions has recently been introduced. This new concept offers many interesting geometric properties for these special functions including logarithmic convexity. The aim of the present paper is to exploit essentially two-dimensional wave propagation in the earth-ionosphere wave path using k-symbol Airy functions (KAFs) in the open unit disk. It is shown that the standard wave-mode working formula may be determined by orthogonality considerations without the use of intricate justifications of the complex plane. By taking into account the symmetry-convex depiction of the KAFs, the formula combination is derived. [ABSTRACT FROM AUTHOR]

A special function is a function that is typically entitled after an early scientist who studied its features and has a specific application in mathematical physics or another area of mathematics. There are a few significant examples, including the hypergeometric function and its unique species. These types of special functions are generalized by fractional calculus, fractal, q-calculus, (q , p) -calculus and k-calculus. By engaging the notion of q-fractional calculus (QFC), we investigate the geometric properties of the generalized Prabhakar fractional differential operator in the open unit disk ∇ : = { ξ ∈ C : | ξ | < 1 } . Consequently, we insert the generalized operator in a special class of analytic functions. Our methodology is indicated by the usage of differential subordination and superordination theory. Accordingly, numerous fractional differential inequalities are organized. Additionally, as an application, we study the solution of special kinds of q–fractional differential equation. [ABSTRACT FROM AUTHOR]

The topics studied in the geometric function theory of one variable functions are connected with the concept of Symmetry because for some special cases the analytic functions map the open unit disk onto a symmetric domain. Thus, if all the coefficients of the Taylor expansion at the origin are real numbers, then the image of the open unit disk is a symmetric domain with respect to the real axis. In this paper, we formulate the q-differential operator associated with the q-Raina function using quantum calculus, that is the so-called Jacksons' calculus. We establish a new subclass of analytic functions in the unit disk by using this newly developed operator. The theory of differential subordination inspired our approach; therefore, we geometrically explore the most popular properties of this new operator: subordination properties, coefficient bounds, and the Fekete-Szegő problem. As special cases, we highlight certain well-known corollaries of our primary findings. [ABSTRACT FROM AUTHOR]

The present investigation is aimed at defining different classes of analytic functions and conformable differential operators in view of the concept of locally fractional differential and integral operators. We present a novel generalized class of analytic functions, which we call it locally fractional analytic functions in the open unit disk. For the suggested class, we look at conditions to get the starlikeness and convexity properties. [ABSTRACT FROM AUTHOR]

The study of chaotic constructions and their associated cryptographic frameworks has sparked a lot of research interest in recent years. Latest advances in wireless technology and the proliferating limitations posed by open communication channels, biometric-enabled remote client authentication procedures with passwords have recently gained traction. In order to address this problem, this paper proposes a secure biometric-based remote user authentication procedure using convolution-Chebyshev chaotic maps with a key agreement procedure. The extended convolution-Chebyshev chaotic maps-based scheme was developed over the interval (- ∞ , + ∞) , and the required properties for the procedure were verified rigorously. The proposed procedure provides a secure client authentication mechanism using biometrics. Additionally, the projected procedure provides a good key agreement feature with perfect forward secrecy while reducing the computation loads for smart cards. As a result, the proposed procedure outperforms related authentication procedures in terms of security and computational performance. [ABSTRACT FROM AUTHOR]

We used the concept of quantum calculus (Jackson's calculus) in a recent note to develop an extended class of multivalent functions on the open unit disk. Convexity and star-likeness properties are obtained by establishing conditions for this class. The most common inequalities of the proposed functions are geometrically investigated. Our approach was influenced by the theory of differential subordination. As a result, we called attention to a few well-known corollaries of our main conclusions. [ABSTRACT FROM AUTHOR]

The recent technological advancement and rapid development of computer networks have increased the popularity of remote password authentication protocols. Toward this end, the emphasis has shifted to protocols that apply to smart cards-empowered multi-server environments. In order to defend against the replay attack, these protocols usually depend on the nonce or timestamp. In this paper, an efficient Mittag–Leffler–Chebyshev Summation Chaotic Map (MLCSCM)-enabled multi-server authentication protocol with the key agreement is proposed and generalized to address this peculiarity in multi-server-oriented applications. The security proof and efficiency analysis of the presented MLCSCM authenticated key agreement protocol is rigorously derived and validated. Compared to the recently published literature, the proposed protocol presents high efficiency with unique features, and it is highly resistant to sophisticated attacks and achieves perfect forward secrecy. [ABSTRACT FROM AUTHOR]

Numerous investigations are introduced to designate the growth dynamic of coronavirus (GDC). We aim to study the dynamic system in view of the fractional calculus in terms of the Caputo-Fabrizio derivative. The flexibility of this operator implies more information and application regarding the dynamic system. Our study will be in two directions, the first one is to suggest the fractional dynamic system without perturbation and the second part is to include a perturbation terms. [ABSTRACT FROM AUTHOR]

In a complex domain, the investigation of the quantum differential subordinations for starlike functions is newly considered by few research studies. In this note, we arrange a set of necessary conditions utilizing the concept of the quantum differential subordinations for starlike functions related to the set of parametric Julia functions. Our method is based on the usage of quantum Jack lemma, where this lemma is generalized recently by the quantum derivative (Jackson calculus). We illustrate a starlike formula dominated by different types of Julia functions. The sufficient conditions are computed in the quantum and the Julia fractional parameters. We indicate a relationship between these two parameters. [ABSTRACT FROM AUTHOR]

It has been reported that there are seven different types of coronaviruses realized by individuals, containing those responsible for the SARS, MERS, and COVID-19 epidemics. Nowadays, numerous designs of COVID-19 are investigated using different operators of fractional calculus. Most of these mathematical models describe only one type of COVID-19 (infected and asymptomatic). In this study, we aim to present an altered growth of two or more types of COVID-19. Our technique is based on the ABC-fractional derivative operator. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion between infected and asymptomatic people. The consequence is accordingly connected with a macroscopic rule for the individuals. In this analysis, we utilize the concept of a fractional chain. This type of chain is a fractional differential–difference equation combining continuous and discrete variables. The existence of solutions is recognized by formulating a matrix theory. The solution of the approximated system is shown to have a minimax point at the origin. [ABSTRACT FROM AUTHOR]

A generalized differential operator utilizing Raina's function is constructed in light of a certain type of fractional calculus. We next use the generalized operators to build a formula for analytic functions of type normalized. Our method is based on the concepts of subordination and superordination. As an application, a class of differential equations involving the suggested operator is studied. As seen, the solution is provided by a certain hypergeometric function. We also create a fractional coefficient differential operator. Its geometric and analytic features are discussed. Finally, we use the Jackson's calculus to expand the Raina's differential operator and investigate its properties in relation to geometric function theory. [ABSTRACT FROM AUTHOR]

Newly, numerous investigations are considered utilizing the idea of parametric operators (integral and differential). The objective of this effort is to formulate a new 2D-parameter differential operator (PDO) of a class of multivalent functions in the open unit disk. Consequently, we formulate the suggested operator in some interesting classes of analytic functions to study its geometric properties. The recognized class contains some recent works. [ABSTRACT FROM AUTHOR]

The central purpose of this effort is to investigate analytic and geometric properties of a class of normalized analytic functions in the open unit disk involving Bernoulli's formula. As a consequence, some solutions are indicated by the well-known hypergeometric function. The class of starlike functions is investigated containing the suggested class. [ABSTRACT FROM AUTHOR]

Newly, the field of fractional differential operators has engaged with many other fields in science, technology, and engineering studies. The class of fractional differential and integral operators is considered for a real variable. In this work, we have investigated the most applicable fractional differential operator called the Prabhakar fractional differential operator into a complex domain. We express the operator in observation of a class of normalized analytic functions. We deal with its geometric performance in the open unit disk. [ABSTRACT FROM AUTHOR]

Saint-Venant equations describe the flow below a pressure surface in a fluid. We aim to generalize this class of equations using fractional calculus of a complex variable. We deal with a fractional integral operator type Prabhakar operator in the open unit disk. We formulate the extended operator in a linear convolution operator with a normalized function to study some important geometric behaviors. A class of integral inequalities is investigated involving special functions. The upper bound of the suggested operator is computed by using the Fox-Wright function, for a class of convex functions and univalent functions. Moreover, as an application, we determine the upper bound of the generalized fractional 2-dimensional Saint-Venant equations (2D-SVE) of diffusive wave including the difference of bed slope. [ABSTRACT FROM AUTHOR]

[Display omitted] The Internet of Things (IoT) comprises of various smart devices for the sharing of sensed data through online services. People will be directly contacted to check their health parameters and the reports will be collected centrally through smart devices. The requirement is protection of messages during the exchange of data between sender and receiver in order to tackle human malicious attacks. Various signature-based schemes are discussed in the literature to provide secure communication. Smart devices however require lightweight tasks by ensuring critical safety strengths. An important problem in the signature based method is that it incurs more computational expenses for signing and verification process in large numbers. In this study, we introduced an efficient Short Signature Scheme (SSS) that uses Fractional Chaotic Map (FCM) for secure communication in IoT based smart devices, the security of which is closely related to a random oracle based on FCM assumption. In this study, we have designed new short signature scheme using FCM. The presented scheme consist of four sub-algorithm as follows: setup, key generation, signing and verification. We have used less rigorous operations based on the FCM to carry out signing and verification procedures, similar to human signing on valid documents and then verifying them as per witness. The proposed SSS offers a better security assurance than currently established signature schemes. The key advantage of the SSS over the DSA schemes is that at the verification stage and signing period it takes less computation; it retains the degree of protection. The presented SSS takes less bandwidth for storage, communication, and computing resources; particularly applicable to wireless devices and smart cards. We concluded that the uses of fractional chaotic maps is more effective for secure communication in human-centered IoT to present a provably secure short signature technique. [ABSTRACT FROM AUTHOR]

In this note, we formulate a new linear operator given by Airy functions of the first type in a complex domain. We aim to study the operator in view of geometric function theory based on the subordination and superordination concepts. The new operator is suggested to define a class of normalized functions (the class of univalent functions) calling the Airy difference formula. As a result, the suggested difference formula joining the linear operator is modified to different classes of analytic functions in the open unit disk. [ABSTRACT FROM AUTHOR]

The idea of an internet of things (IoT)-based smart city evolves with the aim of improving the quality of citizens' lives through the practice of data and announcement (such as email, connection, etc.) tools. The idea of smart cities is believed to be feasible through the incorporation of new technologies such as IoT, automation and machine learning in which IoT plays a key role. When billions of slight strategies drive online and start sharing their information, confirmation has already described as a major security issue nearby the IoT. To exacerbate things, as internet technology advances, advanced hacker methods and new forms of threats arise after each other. It is, therefore, necessary to create efficient authentication protocol that is simpler and easier in order to free users from their anxiety and enhance their user experience. Smart card-based key authentication protocols have formed the normal in the latest years, featuring their exceptionally lightweight, easy-to-use equipment and low-cost apps. We proposed an efficient robust authentication protocol using the extended chaotic map in this article. The security of the proposed authentication protocol formally and informally evaluated to demonstrate robustness. Examination of the quality of the proposed authentication protocol has also given sufficient care of demonstrating the possibility of application in real-time requests. [ABSTRACT FROM AUTHOR]

There are different approaches that indicate the dynamic of the growth of microbe. In this research, we simulate the growth by utilizing the concept of fractional calculus. We investigate a fractional system of integro-differential equations, which covers the subtleties of the diffusion between infected and asymptomatic cases. The suggested system is applicable to distinguish the presentation of growth level of the infection and to approve if its mechanism is positively active. An optimal solution under simulation mapping assets is considered. The estimated numerical solution is indicated by employing the fractional Tutte polynomials. Our methodology is based on the Atangana–Baleanu calculus (ABC). We assess the recommended system by utilizing real data. [ABSTRACT FROM AUTHOR]

The developments in telecommunication and online facility resolutions help to connect the digital divide among urban and rural healthcare services administrations, empowering arrangement of appropriate medicinal finding and treatment discussions. Mobile-healthcare (m-Healthcare) systems can be used for quality improvement of healthcare and monitoring individuals with chronic diseases like heart disease and diabetes under medical affair. Wireless body area networks are installed in the human body, which transmit the information via Bluetooth or other means to the smartphone. In this study, we introduce a new efficient mobile-healthcare emerging emergency medical system using conformable chaotic maps under cloud computing environment. [ABSTRACT FROM AUTHOR]

In this effort, we propose a new fractional differential operator in the open unit disk. The operator is an extension of the Atangana-Baleanu differential operator without singular kernel. We suggest it for a normalized class of analytic functions in the open unit disk. By employing the extended operator, we study the time-2-D space heat equation and optimizing its solution by a chaotic function. [ABSTRACT FROM AUTHOR]

Symmetric operators have benefited in different fields not only in mathematics but also in other sciences. They appeared in the studies of boundary value problems and spectral theory. In this note, we present a new symmetric differential operator associated with a special class of meromorphically multivalent functions in the punctured unit disk. This study explores some of its geometric properties. We consider a new class of analytic functions employing the suggested symmetric differential operator. [ABSTRACT FROM AUTHOR]

We present an analytic solvability of a class of Langevin differential equations (LDEs) in the asset of geometric function theory. The analytic solutions of the LDEs are presented by utilizing a special kind of fractal function in a complex domain, linked with the subordination theory. The fractal functions are suggested for the multi-parametric coefficients type motorboat fractal set. We obtain different formulas of fractal analytic solutions of LDEs. Moreover, we determine the maximum value of the fractal coefficients to obtain the optimal solution. Through the subordination inequality, we determined the upper boundary determination of a class of fractal functions holding multibrot function ...(z) = 1 + 3k z + z³. [ABSTRACT FROM AUTHOR]

In this paper, we define a new differential-difference operator in the open unit disk. This operator describes the analytic geometric representation of the solution of the well known Beltrami differential equation in a complex domain, which this type of equations usually employs in image processing. Moreover, topological properties such as boundedness and compactness are introduced in different spaces such as Hardy space and Blog space. [ABSTRACT FROM AUTHOR]

Recently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is based on the concept of conformable calculus, which involves this term. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion among infected and asymptomatic characters. Strong control is considered due to the social separation. The result is consequently associated with a macroscopic law for the population. This dynamic system is useful to recognize the behavior of the growth rate of the infection and to confirm if its control is correctly functioning. A unique solution is studied under self-mapping properties. The periodicity of the solution is examined by using integral control and the optimal control is discussed in the sequel. [ABSTRACT FROM AUTHOR]

In this note, we establish the existence of solutions in the moment mode of a fractional evolution equation, as well as a fractional coupled system, obtained by new Krasnoselskii type fixed point and coupled fixed point theorems. We use new Krasnoselskii type contraction conditions in the sense of measure of noncompactness in Banach spaces. The new outcomes extend some special well known recent results. [ABSTRACT FROM AUTHOR]

The studies in operator theory are attracting many researchers. The central aim of this investigation is to formulate a special parametric differential operator (PDO) based on the error function in the open unit disk. The suggested operator is related to the well-known Carlson–Shaffer operator and the differential operator due to Salagean. We express a class of analytic functions to study its performance in view of the geometric function theory. As application, we employ PDO to present the conformable d'Alembert's equation. We discuss the univalent solution of the suggested equation and study some of its geometric behaviours. [ABSTRACT FROM AUTHOR]

In this paper, we discuss fixed point theorems for a new χ-set contraction condition in partially ordered Banach spaces, whose positive cone K is normal, and then proceed to prove some coupled fixed point theorems in partially ordered Banach spaces. We relax the conditions of a proper domain of an underlying operator for partially ordered Banach spaces. Furthermore, we discuss an application to the existence of a local fractional integral equation. [ABSTRACT FROM AUTHOR]

The present investigation covenants with the concept of quantum calculus besides the convolution operation to impose a comprehensive symmetric q -differential operator defining new classes of analytic functions. We study the geometric representations with applications. The applications deliberated to indicate the certainty of resolutions of a category of symmetric differential equations type Briot-Bouquet. [ABSTRACT FROM AUTHOR]

Lately, many studies were offered to introduce the population dynamics of COVID-19. In this investigation, we extend different physical conditions of the growth by employing fractional calculus. We study a system of coupled differential equations, which describes the dynamics of the infection spreading between infected and asymptomatic styles. The healthy population properties are measured due to the social meeting. The result is associated with a macroscopic law for the population. This dynamic system is appropriate to describe the performance of growth rate of the infection and to verify if its control is appropriately employed. A unique solution, under self-mapping possessions, is investigated. Approximate solutions are presented by utilizing fractional integral of Chebyshev polynomials. Our methodology is based on the Atangana–Baleanu calculus, which provides various activity results in the simulation. We tested the suggested system by using live data. We found positive action in the graphs. [ABSTRACT FROM AUTHOR]

Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators, integral operators, and classes of analytic functions, especially the classes that are generated by convolution product (Hadamard product). In this effort, we aim to introduce a quantum symmetric conformable differential operator (Q-SCDO). This operator generalized some well-know differential operators such as Sàlàgean differential operator. By employing the Q-SCDO, we present subclasses of analytic functions to study some of its geometric solutions of q-Painlevé differential equation (type III). [ABSTRACT FROM AUTHOR]

The purpose of this article is to introduce a new general family of normalized analytic fractal function in the open unit disk. We employ this class to define a fractional differential operator of two fractals. This operator, under some conditions involves the well known Salagean differential operator. Our method is based on the Hadamard product and its generalization of functions with negative coefficients. [ABSTRACT FROM AUTHOR]

Inequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel. [ABSTRACT FROM AUTHOR]

The economic order quantity (EOQ) is the order quantity that minimizes the total holding costs and ordering costs. In this effort, we propose a design for EOQ by employing a conformable differential-difference operator, which accepts to minimize the EOQ. [ABSTRACT FROM AUTHOR]

In current realization, our object is to use the convolution product in terms of the notion quantum calculus to deliver a propagated q-derivative factor taking a more generalized Sàlàgean formula. By joining both the new factor together with the Janowski formula, we designate a special category of analytic factors in domain of unit disk. Finally, we deliberate a set of significant inequalities involving these classes. As applications, we seek the q-differential translator to generalize a denomination of differential equations species Briot-Bouquet and formulate its upper analytic solution using the subordination idea. This application can be employed in information theory and thermo dynamical systems. [ABSTRACT FROM AUTHOR]

In our current investigation, we apply the idea of quantum calculus and the convolution product to amend a generalized Salagean q-differential operator. By considering the new operator and the typical version of the Janowski function, we designate definite new classes of analytic functions in the open unit disk. Significant properties of these modules are considered, and recurrent sharp consequences and geometric illustrations are realized. Applications are considered to find the existence of solutions of a new class of q-Briot–Bouquet differential equations. [ABSTRACT FROM AUTHOR]

We set up the existence of a symmetric outcome of a system of simultaneous nonlinear fractional integral equations, that arises in motion of water wave on smooth surface, with the help of a common fixed point theorem satisfying a generalized FG-contractive condition. To accomplish this, we introduce first the concept of generalized FG-contractive condition for two pairs of self-mappings in a complete metric space and then we establish requisites for common fixed point results for weakly compatible mappings followed by a suitable example. [ABSTRACT FROM AUTHOR]

AbstractIn this paper we define a Bernardi type quantum integral operator. It transforms the starlike univalent in the unit disk into a starlike region in it. We show that the upper-bound of the third-order Hankel determinant for classes of q-starlike functions is connected with a q-analogue integral operator, defined by a modified q-Bernardi integral operator. The Fekete-Szegö inequality of these classes is also investigated. Numerous well-known specific instances, examples and graphics are listed in the paper. The computations are done by Mathematica 13.3. [ABSTRACT FROM AUTHOR]