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.

In this work, an algorithm for finding numerical solutions of linear fractional delay-integro-differential equations (LFDIDEs) variable-order (VO) is introduced. The operational matrices are used as discretization technique based on shifted Chebyshev polynomials (SCPs) the first kind with spectral collocation method. proposed VO-LFDIDEs have multiterms integer, fractional-order derivatives dela...

Abstract In this research study, we investigate the existence and uniqueness of solutions for a coupled multiorder system fractional differential equations involving integro-differential boundary conditions in Riemann–Liouville setting. The presented results are obtained via classical Banach principle along with Leray–Schauder Krasnosel’skiĭ’s fixed-point theorems. Examples included to support ...

We present a relatively new and very efficient method to find approximate analytical solutions for general class of nonlinear fractional Volterra Fredholm integro-differential equations. The test problems included the comparison with previous results by other methods clearly illustrate simplicity accuracy method.

‎In this article‎, we use a finite difference technique‎ ‎to solve variable-order fractional integro-differential equations‎ ‎(VOFIDEs‎, ‎for short)‎. ‎In these equations‎, ‎the variable-order fractional integration(VOFI) and‎ ‎variable-order fractional derivative (VOFD) are described in the‎ ‎Riemann-Liouville's and Caputo's sense,respectively‎. ‎Numerical experiments‎, ‎consisting of two exam...

We formulate and prove a non-local “maximum principle for semicontinuous functions” in the setting of fully nonlinear and degenerate elliptic integro-partial differential equations with integro operators of second order. Similar results have been used implicitly by several researchers to obtain comparison/uniqueness results for integro-partial differential equations, but proofs have so far been...

This work studies the existence and p-th moment asymptotic stability of mild solution some neutral fractional stochastic integro-differential equations involving non-instantaneous impulses Poisson jumps. Sufficient conditions proving solutions are obtained utilizing analysis, resolvent operator Krasnoselskii-Schaefer type fixed point theorem.

a method for solving a class of weakly singular volterra integral equations is given by using the fractional differential transform method. the approximate solution of these equa­tions is calculated in the form of a finite series with easily computable terms. while in some examples this series solution increased up to the exact closed solution, in some other examples, we can see the accuracy an...

the purpose of this study is to present an approximate numerical method for solving high order linear fredholm-volterra integro-differential equations in terms of rational chebyshev functions under the mixed conditions. the method is based on the approximation by the truncated rational chebyshev series. finally, the effectiveness of the method is illustrated in several numerical examples. the p...