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In this research, we investigate the existence of solution for a class of coupled fractional impulsive hybrid integro-differential equations with hybrid boundary conditions. Our primary tools for this analysis are the Banach contraction mapping principle (BCMP) and Schaefer’s fixed point theorem. This study ended with two applied examples to facilitate understanding of the theoretical results obtained. [ABSTRACT FROM AUTHOR]

In this article, we implemented the idea of a fuzzy interval-valued function with the well-known generalized fuzzy fractional operators, associated with different types of convexities and preinvexities. We developed the Prabhakar fuzzy fractional operators using the fuzzy interval-valued function. We presented the novel extensions of Hermite-Hadamard fuzzy-type and trapezoidal fuzzy-type inequalities, based on the h-Godunova-Levin convex and h-Godunova preinvex fuzzy interval-valued functions. [ABSTRACT FROM AUTHOR]

This paper studies the integro-differential equations of Hilfer fractional (HF) neutral stochastic evolution on an infinite interval with almost sectorial operators and their attractive solutions. We use semigroup theory, stochastic analysis, compactness methods, and the measure of noncompactness (MNC) as the foundation for our methodologies. We establish the existence and attractivity theorems for mild solutions by considering the fact that the almost sectorial operator is both compact and noncompact. Example that highlight the key findings are also provided. [ABSTRACT FROM AUTHOR]

This paper investigates some well-known inequalities for q-h-integrals. These include Hölder, Ostrowski, Grüss and Opial type inequalities. Refinement of the Hadamard inequality for q-h-integrals is also established by applying the definition of strongly convex functions. From main theorems, q-Hölder, q-Ostrowski and q-Grüss inequalities can be obtained in particular cases. [ABSTRACT FROM AUTHOR]

In this article, we discuss the findings of new developments in a class of new triangular functions that blend the quantity functions of the traditional triangular. Considering the significant role played by the triangular functions in applied mathematics, physics, and engineering, it is conceivable to predict that the theory of new triangular functions will provide us with additional interpretations and discoveries in mathematics and physics. The solutions which consider variable separation based on arbitrary functions are constructed to the (3+1)-dimensional Burgers model by presenting the Fibonacci Riccati technique and the linearly independent variable separation approach. This technique's fundamental concept is to describe the solution of the Burgers model as a polynomial in the Riccati Equation solution that satisfies the symmetrical hyperbolic and triangular Fibonacci functions. Depending on the choice of suitable functions for variable separation, an abundance of new localized solutions were obtained. Moreover, examples such as embedded solitons, rectangle-solitons, plateau-type ring solitons, taper-like solitons, and their interactions with each other, following the symmetrical hyperbolic and triangular Fibonacci functions, as well as the golden mean, could be explored. [ABSTRACT FROM AUTHOR]

In this study, we use an effective meshless method to estimate the numerical solution of 3-D time-fractional Sobolev equation. The recommended meshless method is used for the spatial derivatives while the Liouville-Caputo derivative technique is utilized for the time derivative portion of the model equation. Accuracy of the method is assessed via error norms and comparison is made with the exact solution and other numerical methods given in more current literature, which demonstrated that the suggested strategy produces excellent performance and is more computationally efficient. [ABSTRACT FROM AUTHOR]

The impact of coupled stress casson nanofluid-flow over a stretching surface will be examined in this paper. The fundamental controlling PDE are transformed using the stated similarity transformation into a pair of coupled, non-linear ODE, one for velocity and the other for temperature distribution. The modeled flow problem's approximate analytical solution was discovered using the approximate analytical approach. Graphs are used to illustrate the effects of different factors. A table illustrating the relationship between the Nusselt number and skin friction is provided. [ABSTRACT FROM AUTHOR]

We focused on the analytical analysis of steady flow of nanofluid, viscous dissipation with convective boundary condition in this work. The MWCNT and SWCNT are used to described the nanofluid. A similarity transformation is applied to convert nonlinear PDE from their dimensional form to dimensionless nonlinear ODE. The developed nonlinear ODE for velocity and temperature profiles are solved by using an approximate analytical technique called the homotopy asymptotic method. Graphs are used to discuss and illustrate the results. Graphs are used to interpret the effects of several factors. Finally, the skin friction and Nusselt number are illustrated in the form of table. [ABSTRACT FROM AUTHOR]