We study the existence of mild solutions for a class of impulsive fractional partial neutral stochastic integro-differential inclusions with statedependent delay. We assume that the undelayed part generates a solution operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by using the nonlinear alternative of Leray-Schauder type for...

This paper successfully applies the Adomian decomposition  and the modified Laplace Adomian decomposition methods to find  the approximate solution of a nonlinear fractional Volterra-Fredholm integro-differential equation. The reliability of the methods and reduction in the size of the computational work give these methods a wider applicability. Also, the behavior of the solution can be formall...

This article is concerned with the study of a new class hybrid fractional q-integro-difference equations involving Caputo type q-derivatives and Riemann-Liouville q-integrals different orders nonlocal q-integro-initial condition. An existence result for given problem obtained by means Krasnoselskii’s fixed point theorem, whereas uniqueness its solutions shown applying Banach contraction mapping...

Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often ...

He’s variational iteration method [1, 2], which is a modified general Lagrange multiplier method [3], has been shown to solve effectively, easily and accurately a large class of nonlinear problems with approximations which converge quickly to accurate solutions. It was successfully applied to autonomous ordinary differential equations [4], nonlinear partial differential equations with variable ...

This paper deals with obtaining some sufficient conditions for oscillation of high-order neutral fractional integro-differential equations. The obtained results are mentioned the first time in literature Caputo–Fabrizio Finally, illustrative examples given to verify our main results.

We establish interior and up to the boundary Hölder regularity estimates for weak solutions of Dirichlet problem fractional g−Laplacian with bounded right hand side g convex. These are first results available in literature integro-differential equations context Orlicz–Sobolev spaces.

In this paper, we investigate the oscillation of a class generalized proportional fractional integro-differential equations with forcing term. We present sufficient conditions to prove some criteria in both Riemann-Liouville and Caputo cases. Besides, numerical examples for applicability our results.

Abstract In this paper, using necessary and sufficient conditions, the new concept of Stepanov µ -pseudo almost automorphic functions ergodicity results, we investigate existence mild bounded solutions for a class fractional integro-differential equations in sense Weyl derivative Banach space.

We apply the Radu–Miheţ method derived from an alternative fixed-point theorem with a class of matrix-valued fuzzy controllers to approximate fractional Volterra integro-differential equation ψ-Hilfer derivative in k-normed spaces obtain approximation for this type equation.