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...

The article deals with the existence of solutions an integro-differential equation in case anomalous diffusion negative Laplace operator a fractional power presence transport term. proof is based on fixed point technique. Solvability conditions for elliptic operators without Fredholm property unbounded domains are used. We discuss how introduction term impacts regularity solutions.

Recently, many papers in the theory of univalent functions have been devoted to mapping and characterization properties of various linear integral or integro-differential operators in the class S (of normalized analytic and univalent functions in the open unit disk U), and in its subclasses (as the classes S∗ of the starlike functions and K of the convex functions in U). Among these operators, ...

A novel and effective method based on Haar wavelets and Block Pulse Functions (BPFs) is proposed to solve nonlinear Fredholm integro-differential equations of fractional order. The operational matrix of Haar wavelets via BPFs is derived and together with Haar wavelet operational matrix of fractional integration are used to transform the mentioned equation to a system of algebraic equations. Our...

We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q ∈ 1, 2 based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the n-term approximation. At the same time, the n-term approximation ...

In this article, we study the asymptotical stability in p-th moment of mild solutions to a class of fractional impulsive partial neutral stochastic integro-differential equations with state-dependent delay in Hilbert spaces. We assume that the linear part of this equation generates an α-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence and as...

*Correspondence: [email protected] 2Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Cankaya University, Ankara, 06530, Turkey 3Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia Full list of author information is available at the end of the article Abstract In this paper, we investigate the...