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Generally, fractional partial integro-differential equations (FPIDEs) play a vital role in modeling various complex phenomena. Because of the several applications of FPIDEs in applied sciences, mathematicians have taken a keen interest in developing and utilizing the various techniques for its solutions. In this context, the exact and analytical solutions are not very easy to investigate the solution of FPIDEs. In this article, a novel analytical approach that is known as the Laplace adomian decomposition method is implemented to calculate the solutions of FPIDEs. We obtain the approximate solution of the nonlinear FPIDEs. The results are discussed using graphs and tables. The graphs and tables have shown the greater accuracy of the suggested method compared to the extended cubic-B splice method. The accuracy of the suggested method is higher at all fractional orders of the derivatives. A sufficient degree of accuracy is achieved with fewer calculations with a simple procedure. The presented method requires no parametrization or discretization and, therefore, can be extended for the solutions of other nonlinear FPIDEs and their systems.

In this paper, we derive some error estimates of Simpson's second type quadrature formula for functions of bounded variation and Lipschitzian mappings. Also, similar error estimations for absolutely continuous functions whose first derivatives belong to Lp[γ, δ] with (p < 1 ≤ ∞) are established. Finally, with the help of the results given in this work, some Simpson's type inequalities involving special means are presented. [ABSTRACT FROM AUTHOR]

In this paper, we consider a pseudo‐parabolic equation with the Caputo fractional derivative. We study the existence and uniqueness of a class of mild solutions of these equations. For a nonlinear problem, we first investigate the global solution under the initial data u0 ∈ L2. In the case of initial data u0 ∈ Lq, q ≠ 2, we obtain the local existence result. Our main tool here is using fundamental tools, namely, Banach fixed point theorem and Sobolev embeddings. In addition, we give an example to illustrate the effectiveness of the method has been proposed. [ABSTRACT FROM AUTHOR]

There are several applications for electro-osmotic MHD flow of hybrid Ferrofluid in the present era, notably in the biochemical as drug delivery systems, microfluidic devices, biomedical diagnostics, microscale systems and medical industries. The electro-osmotic MHD flow of a hybrid Ferrofluid containing Cobalt Ferrite, magnetite nanoparticles via a vertically inclined microchannel is investigated in this study. In furthermore, the perpendicular magnetic field is considered. Investigations are also carried into the effects of mass and heat transfer in this moving fluid. Partial differential equations provide as a representation for the aforementioned physical phenomenon, using suitable dimensionless nondimensional variables. Also, the classical system is fractionalized using the generalized Fourier and Fick's law. Generalizations are made based on the account of the Caputo derivative. The solution for the velocity, concentration, and temperature outlines is developed by using the Fourier and Laplace techniques. Moreover, the parametric impact of many physical factors as the Brinkman parameter, the temperature, velocity, concentration and stress parameters (Schmidt, Grashof, and Prandtl numbers). Graphs and discussions of concentration distributions is also discussed. The Sherwood number, rate of heat transmission, and skin friction are calculated and summarized. Since the fractional models are more accurate, they also provide a broader variety of possible solutions. Considering the relevant data, these solutions could be the best. Additionally, the heat transfer rate is higher as compare to nanofluid and regular fluid. The Hybrid Ferrofluid having capability to control velocity boundary layer rapidly as compare to nanofluid and regular fluid. [ABSTRACT FROM AUTHOR]

In this article, we propose a viscosity-type scheme for approximating a common solution of convex minimization problem, monotone vector field inclusion problem and fixed point problem involving multi-valued nonexpansive mapping in the framework of Hadamard spaces. We obtain a strong convergence theorem for the sequence generated therefrom to a solution of the problem. Furthermore, we apply our results to compute the Fréchet mean, find the mean of probabilities, minimize energy of measurable mappings and solve a problem of two-arm robotic motion control. Finally, we give numerical example to demonstrate the applicability of the method and also issue comparisons with some existing methods. Our results extend and complement some recent results in the literature. [ABSTRACT FROM AUTHOR]

In this article, a generalized variational inequality problem in the setting of Hadamard spaces is introduced and analyzed. For approximating a solution of the problem when the underlined mapping is monotone, an adaptive algorithm that requires the computation of only one proximal operator at each iteration is proposed. The work gives a step towards investigating monotone variational inequality problems in geodesic settings. [ABSTRACT FROM AUTHOR]

The approach described in this research is an exemplar‐based inpainting problem that combines a two‐stage structure tensor and image sparse representation to fill in any missing pixels. An important step is to select the filling order and local intensity smoothness, as well as to ensure that the structure is not destroyed. We employ a two‐stage structure tensor‐based priority for the filling order: finding the candidate patches and determining the appropriate weight of each candidate patch under the constraint of local patch consistency, then applying a blend of a sparse linear combination of candidate patches to fill in the missing region of the image. In addition, this technique may also be used for object removal. The proposed method yields results that are visually natural and qualitative. [ABSTRACT FROM AUTHOR]

In this work, we establish the closedness and convexity of the set of fixed points of equally continuous and asymptotically demicontractive mapping in the intermediate sense. We proposed an inertial hybrid projection technique for determining an approximate common solution to three significant problems. The first is the system of generalized mixed equilibrium problems with relaxed η−ζ$$ \eta -\zeta $$ monotone mappings, the second is the problem of fixed points of a countable family of equally continuous and asymptotically demicontractive mappings in the intermediate sense, and the third is of determining a point in a null space of a countable family of inverse strongly monotone mappings in Hilbert space. Based on these problems, we formulate a theorem and establish its strong convergence to their common solution. Additionally, we studied the applications of our algorithm to variational inequality problems and convex optimization problems. Finally, we numerically demonstrate the efficiency and robustness of our scheme. Several results available in the literature can be obtained as special cases of our result. [ABSTRACT FROM AUTHOR]

Recently, structured nonlinear least-squares (NLS) based algorithms gained considerable emphasis from researchers; this attention may result from increasingly applicable areas of these algorithms in different science and engineering domains. In this article, we coined a new efficient structured-based NLS algorithm. We developed a diagonal Hessian-based formulation for solving NLS problems. We derived the quasi-Newton update based on a diagonal matrix scheme subject to a modified structured secant condition. Also, we show that the algorithm's search direction satisfies a sufficient descent condition under some standard assumptions. Subsequently, we also prove the global convergence of the algorithm and then eventually show its linear convergence rate for strongly convex functions. Furthermore, to show case the proposed algorithm's performance, we experimented numerically by comparing it with other approaches on some benchmark test functions available in the literature. Finally, the introduced scheme is applied to solve some data-fitting problems [ABSTRACT FROM AUTHOR]

In this work, the main discussion centres on avoiding the use of triangle inequality while proving Cauchy sequence to establish best proximity point theorems for single valued as well as multivalued non-self mappings. We prove such best proximity point theorems in the setting of non-triangular metric spaces and elaborate through examples. In this process host of the existing best proximity results are generalized and improved. To arouse further interest in the subject, we connect this work in solving a specific type of partial differential equation problem. [ABSTRACT FROM AUTHOR]

Several conjugate gradient (CG) parameters resulted in promising methods for optimization problems. However, it turns out that some of these parameters, for example, 'PRP,' 'HS,' and 'DL,' do not guarantee sufficient descent of the search direction. In this work, we introduce new spectral-like CG methods that achieve sufficient descent property independently of any line search (LSE) and for arbitrary nonnegative CG parameters. We establish the global convergence of these methods for four different parameters using Wolfe LSE. Our algorithm achieves this without regular restart and assumption of convexity regarding the objective functions. The sequences generated by our algorithm identify points that satisfy the first-order necessary condition for Pareto optimality. We conduct computational experiments to showcase the implementation and effectiveness of the proposed methods. The proposed spectral-like methods, namely nonnegative SPRP, SHZ, SDL, and SHS, exhibit superior performance based on their arrangement, outperforming HZ and SP methods in terms of the number of iterations, function evaluations, and gradient evaluations. [ABSTRACT FROM AUTHOR]

Conjugate gradient techniques are known for their simplicity and minimal memory usage. However, it is known that in the vector optimization context, the Polak-Ribi'ere-Polyak (PRP), Liu-Storey (LS), and Hestenes-Stiefel (HS) conjugate gradient (CG) techniques fail to satisfy the sufficient descent property using Wolfe line searches. In this work, we propose a variation of the PRP, LS, and HS CG techniques that we termed YPR, YLS, and YHS, respectively. These techniques exhibit the desirable property of sufficient descent without line search, except for the YHS which uses Wolfe line search for its sufficient descent property. Under certain standard assumptions and employing strong Wolfe conditions, we investigate the global convergence properties of the proposed techniques. The global convergence analysis extends beyond convexity assumption on the objective functions. Additionally, we present numerical experiments and comparisons to demonstrate the implementation, efficiency, and robustness of the proposed techniques. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified general inertial Mann algorithm and prove that it generates a sequence which converges weakly to a fixed point of a nonexpansive mapping in Hilbert spaces. Moreover, by using the viscosity method, we introduce a general inertial viscosity algorithm and prove that it generates a sequence which converges strongly to a common fixed point of a countable family of nonexpansive operators. We also derive schemes for solving constrained convex optimization, monotone inclusion, and nonsmooth convex optimization problems. Finally, we apply one of our proposed algorithms to solve image restoration problem. [ABSTRACT FROM AUTHOR]

In this work, two inertial algorithms for approximating common elements of the sets of solutions of three important problems are constructed. The first problem is a generalized mixed equilibrium one involving relaxed monotone mapping, the second is a zero problem of inverse strongly monotone mappings, while the third one is a fixed point problem of a family of relatively nonexpansive mappings. The first algorithm is a shrinking projection type for a common solution of all the three problems. The second is a generalized Alber projection free method for the second and the third problems. Each of the devised algorithms uses the conjugate gradient-like direction, which allows it to accelerate its iterates toward a solution of the problems. The strong convergence theorem for each of the algorithms is formulated and proved in a real 2 - uniformly convex and uniformly smooth Banach space. Additionally, the applications of our algorithms to convex optimization problems and image recovery problems are studied. The advantages and computational efficiency of our methods are analyzed based on their numerical performance in comparison to some of the existing and recently proposed methods using numerical example. [ABSTRACT FROM AUTHOR]

In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various characterizations and explore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specifically, we establish that these mappings are Lipschitz continuous, satisfying the demiclosedness-type property, and possessing a closed convex fixed point set. Furthermore, we show that the fixed points of the mappings can be effectively approximated using an iterative scheme for fixed points of nonexpansive mappings. The results in this work contribute to a deeper understanding of strictly pseudocontractive mappings and their applicability in the context of fixed point theory in metric spaces. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to construct a common solution of the split null point problem associated with the maximal monotone operators and the fixed point problem associated with a finite family of k‐demicontractive operators in Hilbert spaces. We compute the optimal common solution via inertial parallel hybrid algorithm under a suitable set of control conditions. The viability of parallel implementation of the algorithm is demonstrated for various theoretical as well as numerical results. The results presented in this paper improve various existing results in the current literature. [ABSTRACT FROM AUTHOR]

Mineral Oil [MO] has significant importance because of its vast variety of applications in various arenas of manufacturing, technology, and industrial processes. The applications of the Mineral Oil [MO] are PVC production, polystyrene production, as a lubricating, cutting fluid, thermoplastics rubber production, glossing product, wood products, cleaning products, lamp oil, glues, toys, veterinary, cosmetics, food preparation, as a brake fluid in some cars, and so forth. Due to these applications of Mineral Oil [MO], in the existing work, the two-dimensional mixed convective flow of micropolar fluid with the applications of the aluminum oxide nanoparticles in a Mineral Oil [MO] base liquid is taken into consideration. The melting heat phenomenon is discussed for the interpretation of heat transmission. Further, the flow analysis is discussed through the impacts of inclined magnetic field, heat generation, Joule heating and thermal radiation. Mass diffusivity is deliberated through the implementation of homogenous and heterogeneous chemical reactions. Entropic behavior is analyzed for the discussion of irreversibility analysis. Suitable similarity transformations are employed to renovate modeled systems of the PDEs into ODEs. Analytical simulation of the proposed model has been accomplished with the utilization of the homotopy analysis technique. Some significant outcomes from the existing work are that the velocity outline is reduced but the energy curve is greater for the melting parameter. Nanofluid entropy generation is increased due to the improvement of the Brinkman parameter and material parameter. Heat transportation is augmented due to the amplification of the radiation parameter, and nanoparticle volume fraction. The present study is useful in different fields of industries, technological processes, mechanical processes, and electrical processes due to the applications of mineral oil. [ABSTRACT FROM AUTHOR]

Nanofluids are used to achieve maximum thermal performance with the smallest concentration of nanoparticles and stable suspension in conventional fluids. The effectiveness of nanofluids in convection processes is significantly influenced by their increased thermophysical characteristics. However, this technology is not ended here; binary and ternary nanofluids are now used to improve the efficiency of regular fluids. Therefore, this paper aims to analyze the natural convection Newtonian ternary nanofluid flow in a vertical channel. The tri‐hybridized nanoparticles of zinc oxide ZnO, Aluminum oxide Al2O3, and titanium oxide TiO2 is dissolved in base fluid distilled water (DW) to form a homogenous suspension. The impact of thermal radiation, joule heating, and viscous dissipation are also assumed. The classical Newtonian ternary nanofluid model has been generalized by using fractal‐fractional derivative (FFD) operator. The generalized model has been discretized by using the Crank–Nicolson scheme and then solved by using computational software. To analyze the behavior of fluid flow and heat distribution in fluid, the obtained solution was computed numerically and then plotted in response to different physical parameters. It is noted from the figure that when the volume fraction ϕ reaches to 0.04 (4% of the base fluid), the ternary nanofluid flow shows a significant amount of enhancement in heat transfer rate as compared to binary and unary nanofluid flows. This enhancement in the rate of heat transfer leads to improve the thermophysical characteristics such as viscosity, thermal expansion, and heat capacity etc. of the base fluid. It is also worth mentioning here that the thermal field is also enhance with the higher values of Eckert number Ec$Ec$, radiation parameter Rd$Rd$, and joule heating parameter Jh${J_h}$. [ABSTRACT FROM AUTHOR]

The Caputo operator has recently gained popularity as a widely used operator in fractional calculus. The purpose of this current research is to develop a new operator by combining the Caputo and proportional derivatives, resulting in the constant proportional Caputo (CPC) fractional operator. To demonstrate the dynamic behavior of this newly defined operator, it was applied to the unsteady Oldroyd‐B fluid model. Additionally, the research considered an Oldroyd‐B fluid in a generalized Darcy medium, considering non‐uniform temperature, radiation, and heat generation. Analytical solutions for the proposed model were obtained and presented in graphical form using the computational software MATHCAD. The impact of various physical parameters was also examined through graphical analysis of velocity and temperature profiles, as well as a comparison between isothermal and non‐uniform temperature. In conclusion, this research found that the CPC fractional operator effectively explains the dynamics of the Oldroyd‐B fluid model with stable and strong memory effects, compared to the classical model. [ABSTRACT FROM AUTHOR]

In recent years, many subclasses of univalent functions, directly or not directly related to the exponential functions, have been introduced and studied. In this paper, we consider the class of S e ∗ for which z f ′ (z) / f (z) is subordinate to e z in the open unit disk. The classic concept of Hankel determinant is generalized by replacing the inverse logarithmic coefficient of functions belonging to certain subclasses of univalent functions. In particular, we obtain the best possible bounds for the second Hankel determinant of logarithmic coefficients of inverse starlike functions subordinated to exponential functions. This work may inspire to pay more attention to the coefficient properties with respect to the inverse functions of various classes of univalent functions. [ABSTRACT FROM AUTHOR]

Diathermal oils have piqued the interest of several researchers in recent years due to their numerous industrial applications. The core aim of this study is the development of a novel fractal-fractional model to analyze the thermal performance of an oil-based tripartite hybrid nanofluid for channel flows. Graphene (Gr), magnesium oxide (MgO), and copper (Cu) nanoparticles are simultaneously dispersed in engine oil to obtain a tripartite hybrid nanofluid. To evaluate the impacts of the shape factor on thermal performance, five different shapes (brick, blade, spherical, platelet, and cylindrical) of nanoparticles are considered. The flow of considered fluid starts due to the constant motion of the right wall, which also encounters constant heating. Meanwhile, the left wall absorbs uniform radiation impacts. The mathematical model to explain this physical process is formulated by utilizing a fractal-fractional derivative, which involves a power-law kernel in its working. This model is exposed to joint employment of classical and fractal Laplace transforms to acquire the analytic solutions. These solutions are further used to develop expressions for skin friction coefficient and Nusselt number. Based on these quantities, heat transfer rate and shear stress are estimated to analyze augmentation in the thermal potential of engine oil and to observe variation in shear stress because of parametric effects. By conducting a comparative analysis between graphs of fractional and fractal-fractional models, it is concluded that a better elucidation of memory effects can be provided through the fractal-fractional approach. Furthermore, this work highlights that dispersing three different types of nanoparticles in engine oil makes it a more effective industrial fluid with a 9.58% higher heat-conduction capacity. This significant enhancement in the thermal performance of engine oil signifies its effectiveness for lubrication and cooling applications. [ABSTRACT FROM AUTHOR]

This paper provides convergence analysis of some variants of the hybrid extragradient algorithm (HEA) in Hilbert spaces. We employ the HEA to compute the common solution of the equilibrium problem and split fixed-point problem associated with the finite families of k -demicontractive mappings. We also incorporate appropriate numerical results concerning the viability of the proposed variants with respect to various real-world applications. [ABSTRACT FROM AUTHOR]

Language is closely connected to the concepts of uncertainty and indeterminacy, as it functions as a fundamental tool for the expression and communication of information. Linguistic formulations possess inherent qualities of ambiguity, imprecision, and vagueness. The comprehension of language frequently hinges upon contextual factors, individual interpretation, and subjective viewpoints, resulting in ambiguities in comprehension. Neutrosophic-linguistic valued hypersoft sets (N-LVHS) play a pivotal role in decision-making by effectively managing linguistic uncertainty, modeling real-world complexity, and accommodating multidimensional information. In the realm of medical diagnosis and treatment, several limitations tied to language and indeterminacy persist. Patients often use vague or imprecise language to describe their symptoms, complicating the accurate identification of ailments. Moreover, diagnostic criteria are subjectively defined, leading to inconsistencies in diagnoses. Disease progression, characterized by its complexity and unpredictability, adds further indeterminacy in treatment planning. The variability in patient responses to treatments introduces uncertainties in outcome prediction. Inconclusive test results and limited clinical data may compound these challenges, underscoring the need for innovative approaches like N-LVHS to address these linguistic and indeterminacy-related limitations and improve the precision and efficacy of medical decision-making and treatment procedures. In constructing an N-LVHS framework for medical diagnosis and treatment, relevant factors, and linguistic terms characterizing medical conditions and treatments are identified. For example, disease severity could be described using terms such as "mild," "moderate," and "severe," while treatment effectiveness may be categorized as "low," "moderate," and "high." Each factor is then assigned neutrosophic values based on their measured impacts. This approach provides a more precise representation of the complex medical diagnostic and treatment landscape. The findings of this study have the potential to assist medical practitioners, researchers, and policymakers in optimizing medical diagnosis and treatment strategies, enhancing patient outcomes, and improving healthcare practices. [ABSTRACT FROM AUTHOR]