Abstract We consider a general class of integro-differential evolution equations which includes the governing equation generalized grey Brownian motion and time- space-fractional heat equation. present relation between parameters distribution underlying stochastic processes, as well discuss different classes processes providing solutions these equations. For subclass equations, containing Maric...

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.

This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel‎. ‎First‎, ‎a collocation method based on Haar wavelets (HW)‎, ‎Legendre wavelet (LW)‎, ‎Chebyshev wavelets (CHW)‎, ‎second kind Chebyshev wavelets (SKCHW)‎, ‎Cos and Sin wavelets (CASW) and BPFs are presented f...

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.

This paper is concerned with the existence and uniqueness of solutions for a new class boundary value problems, consisting by Hilfer-Hadamard fractional differential equations, supplemented nonlocal integro-multipoint conditions. The unique solution obtained via Banach contraction mapping principle, while results are established applying Schaefer Krasnoselskii fixed point theorems as well Leray...

Nature often presents complex dynamics, which cannot be explained by means of ordinary models. In this paper, we establish an approach to certain fractional dynamic systems using only deterministic arguments. The behavior of the trajectories of fractional non-linear autonomous systems around the corresponding critical points in the phase space is studied. In this work we arrive to several inter...