Search

The main aim of this work is to conduct an analysis of the approximate controllability of Hilfer fractional (HF) neutral stochastic differential systems under the condition of an almost sectorial operator with delay. The theoretical ideas linked to stochastic analysis, fractional calculus and semigroup theory, along with the fixed-point technique, are utilized to establish the key results of this article. More precisely, the main theorem of this study is devoted to proving the fact that the relevant linear system is approximately controllable. Finally, to help this research be as comprehensive as possible, we provide a theoretical application and filter system. [ABSTRACT FROM AUTHOR]

In this paper, we study a coupled fully hybrid system of (k , Φ) –Hilfer fractional differential equations equipped with non-symmetric (k , Φ) –Riemann-Liouville (RL) integral conditions. To prove the existence and uniqueness results, we use the Krasnoselskii and Perov fixed-point theorems with Lipschitzian matrix in the context of a generalized Banach space (GBS). Moreover, the Ulam–Hyers (UH) stability of the solutions is discussed by using the Urs's method. Finally, an illustrated example is given to confirm the validity of our results. [ABSTRACT FROM AUTHOR]

Drugs have always been one of the most important concerns of families and government officials at all times, and they have caused irreparable damage to the health of young people. Given the importance of this great challenge, this article discusses a non-symmetric fractal-fractional order ice-smoking mathematical model for the existence results, numerical results, and stability analysis. For the existence of the solution of the given ice-smoking model, successive iterative sequences are defined. The uniqueness of the solution Hyers–Ulam (HU) stability is established with the help of the existing definitions and theorems in functional analysis. By the utilization of two-step Lagrange polynomials, we provide numerical solutions and provide a comparative numerical analysis for different values of the fractional order and fractal order. The numerical simulations show the applicability of the scheme and future prediction and the effects of fractal-fractional orders simultaneously. [ABSTRACT FROM AUTHOR]

In the present paper, we analyze a coupled system of nonlinear three point boundary value problems (BVPs) consisting of a coupled system of higher order hybrid sequential differential equations formulated by fractional operators. We study several new conditions in the direction of existence theory for solutions of the given hybrid system under the weaker hypotheses based on the method of measure of non-compactness in degree theory. The required conditions confirming the uniqueness and stability are derived in relation to the coupled system of hybrid sequential BVPs. Lastly, we extend our hybrid sequential system to a real mathematical model of typhoid treatment with four compartments and by deriving numerical schemes for this generalized hybrid sequential system, we analyze the variations of different fractional orders and their impact on dynamical behaviors of the mentioned hybrid system of typhoid model. [ABSTRACT FROM AUTHOR]

In this article, we consider a fractal-fractional tobacco mathematical model with generalized kernels of Mittag-Leffler functions for qualitative and numerical studies. From qualitative point of view, our study includes; existence criteria, uniqueness of solution and Hyers-Ulam stability. For the numerical aspect, we utilize Lagrange's interpolation polynomial and obtain a numerical scheme which is further illustrated simulations. Lastly, a comparative analysis is presented for different fractal and fractional orders. The numerical results are divided into four figures based on different fractal and fractional orders. We have found that the fractional and fractal orders have a significant impact on the dynamical behaviour of the model. [ABSTRACT FROM AUTHOR]

In recent decades, AIDS has been one of the main challenges facing the medical community around the world. Due to the large human deaths of this disease, researchers have tried to study the dynamic behaviors of the infectious factor of this disease in the form of mathematical models in addition to clinical trials. In this paper, we study a new mathematical model in which the dynamics of CD 4 + T-cells under the effect of HIV-1 infection are investigated in the context of a generalized fractal-fractional structure for the first time. The kernel of these new fractal-fractional operators is of the generalized Mittag-Leffler type. From an analytical point of view, we first derive some results on the existence theory and then the uniqueness criterion. After that, the stability of the given fractal-fractional system is reviewed under four different cases. Next, from a numerical point of view, we obtain two numerical algorithms for approximating the solutions of the system via the Adams-Bashforth method and Newton polynomials method. We simulate our results via these two algorithms and compare both of them. The numerical results reveal some stability and a situation of lacking a visible order in the early days of the disease dynamics when one uses the Newton polynomial. [ABSTRACT FROM AUTHOR]

In this paper, we present the existence criteria for the solutions of boundary value problems involving generalized fractional integro-Langevin equation and inclusion supplemented with nonlocal fractional boundary conditions. The main idea of the current research is to combine the integro-differential and Langevin structures together. The main tools of our study include certain inequalities and well-known fixed point theorems. Numerical examples are constructed to demonstrate the application of the obtained results. [ABSTRACT FROM AUTHOR]

The World Health Organization declared COVID-19 a global pandemic in March 2020, which had a significant impact on global health and economies. There have been several Zika outbreaks in different regions such as Africa, Southeast Asia, and the Americas. Therefore, it is essential to study the dynamics of these two diseases, taking into account their memory and recurrence effects. A new fractal-fractional hybrid Mittag-Leffler model of COVID-19 and Zika co-dynamics is designed and studied to evaluate the effects of COVID-19 on Zika and vice-versa. The stability analysis of the local asymptotic type at disease-free equilibrium is conducted for the hybrid model. The existence of unique solutions to the model is established via some fixed point results. The fractal-fractional model is proved to be Hyers–Ulam stable. With the help of Newton polynomials, we obtain some numerical algorithms to approximate the solutions of the fractal-fractional hybrid Mittag-Leffler model graphically. The impact of fractional and fractal orders on the dynamics of each of the epidemiological classes is also assessed. In addition, empirical evidence from numerical simulations suggests that implementing measures to contain the transmission of the SARS-CoV-2 virus can significantly contribute to the reduction of co-infections involving the Zika virus. Therefore, it is imperative for healthcare systems to maintain a state of constant vigilance in order to detect any atypical patterns or probable occurrences of co-infections, particularly in areas where both diseases are widespread. Additionally, it is vital to consult the most recent directives provided by health authorities, as our comprehension of diseases may undergo advancements over the course of time. [ABSTRACT FROM AUTHOR]

In this paper, we study a new class of nonlinear fractional differential equations with three-point boundary conditions. Existence of solutions are obtained by using Krasnoselskii's fixed point theorem and Leray- Schauder nonlinear alternative. An illustrative example is presented at the end of the paper to illustrate the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, by using the endpoint result for multifunctions, we investigate the existence of solutions for a boundary value problem for fractional differential inclusions with sum and integral boundary conditions. Finally, an example is also given to illustrate the validity of our main result. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel mathematical model for the spread of COVID-19 involving environmental white noise. The new stochastic model was studied for the existence and persistence of the disease, as well as the extinction of the disease. We noticed that the existence and extinction of the disease are dependent on R 0 (the reproduction number). Then, a numerical scheme was developed for the computational analysis of the model; with the existing values of the parameters in the literature, we obtained the related simulations, which gave us more realistic numerical data for the future prediction. The mentioned stochastic model was analyzed for different values of σ 1 , σ 2 and β 1 , β 2 , and both the stochastic and the deterministic models were compared for the future prediction of the spread of COVID-19. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of solutions to a nonlinear boundary value problem (BVP) of variable order at resonance. The main theorem in this study is proved with the help of generalized intervals and piecewise constant functions, in which we convert the mentioned Caputo BVP of fractional variable order to an equivalent standard Caputo BVP at resonance of constant order. In fact, to use the Mawhin's continuation technique, we have to transform the variable order BVP into a constant order BVP. We prove the existence of solutions based on the existing notions in the coincidence degree theory and Mawhin's continuation theorem (MCTH). Finally, an example is provided according to the given variable order BVP to show the correctness of results. [ABSTRACT FROM AUTHOR]

This paper is devoted to generalizing the standard system of Navier boundary value problems to a fractional system of coupled sequential Navier boundary value problems by using terms of the Caputo derivatives. In other words, for the first time, we design a multi-term fractional coupled system of Navier equations under the fractional boundary conditions. The existence theory is studied regarding solutions of the given coupled sequential Navier boundary problems via the Krasnoselskii's fixed-point theorem on two nonlinear operators. Moreover, the Banach contraction principle is applied to investigate the uniqueness of solution. We then focus on the Hyers–Ulam-type stability of its solution. Furthermore, the approximate solutions of the proposed coupled fractional sequential Navier system are obtained via the generalized differential transform method. Lastly, the results of this research are supported by giving simulated examples. [ABSTRACT FROM AUTHOR]

In this paper, we establish several necessary conditions to confirm the uniqueness-existence of solutions to an extended multi-order finite-term fractional differential equation with double-order integral boundary conditions with respect to asymmetric operators by relying on the Banach's fixed-point criterion. We validate our study by implementing two numerical schemes to handle some Riemann–Liouville fractional boundary value problems and obtain approximate series solutions that converge to the exact ones. In particular, we present several examples that illustrate the closeness of the approximate solutions to the exact solutions. [ABSTRACT FROM AUTHOR]

In this research study, we establish some necessary conditions to check the uniqueness-existence of solutions for a general multi-term ψ -fractional differential equation via generalized ψ -integral boundary conditions with respect to the generalized asymmetric operators. To arrive at such purpose, we utilize a procedure based on the fixed-point theory. We follow our study by suggesting two numerical algorithms called the Dafterdar-Gejji and Jafari method (DGJIM) and the Adomian decomposition method (ADM) techniques in which a series of approximate solutions converge to the exact ones of the given ψ -RLFBVP and the equivalent ψ -integral equation. To emphasize for the compatibility and the effectiveness of these numerical algorithms, we end this investigation by providing some examples showing the behavior of the exact solution of the existing ψ -RLFBVP compared with the approximate ones caused by DGJIM and ADM techniques graphically. [ABSTRACT FROM AUTHOR]

A nonlinear quantum boundary value problem (q-FBVP) formulated in the sense of quantum Caputo derivative, with fractional q-integro-difference conditions along with its fractional quantum-difference inclusion q-BVP are investigated in this research. To prove the solutions' existence for these quantum systems, we rely on the notions such as the condensing functions and approximate endpoint criterion (AEPC). Two numerical examples are provided to apply and validate our main results in this research work. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for a new class of fractional q-integro-difference equations involving Riemann-Liouville q-derivatives and a q-integral of different orders, supplemented with boundary conditions containing q-integrals of different orders. The first existence result is obtained by means of Krasnoselskii's fixed point theorem, while the second one relies on a Leray-Schauder nonlinear alternative. The uniqueness result is derived via the Banach contraction mapping principle. Finally, illustrative examples are presented to show the validity of the obtained results. The paper concludes with some interesting observations. [ABSTRACT FROM AUTHOR]