In this study, we develop a theory for the nonlocal hybrid boundary value problem fractional integro-differential equations featuring Atangana–Baleanu derivatives. The corresponding integral equation is presented. Then, establish existence results using Dhage’s fixed point theorem sum of three operators. We also offer additional exceptional cases and similar outcomes. order to demonstrate verif...

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...

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.

The main purpose of this paper is to consider Adomian's decomposition method in non-linear Volterra integro-differential equations. The advantages of this method, compared with the recent numerical techniques (in particular the implicitly linear collocation methods) , and the convergence of Adomian's method applied to such nonlinear integro-differential equations are discussed. Finally, by ...

in this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional volterra-fredholm integro-differential equations. here, we use the so-called two-dimensional block-pulse functions.first, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. then, by using this matrices, the nonlinear two-dimensional vol...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

in this article, we study the analytical solutions of different parabolic heat equations with different boundaryconditions in the form of multi-term fractional differential equations. then we compare these analytical solutions with numerical finite difference methods. this comparison demonstrates the accuracy of the analytical and numerical methods presented here.

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.