In this research, the finite difference method is used to solve initial value problem of linear first order Volterra-Fredholm integro-differential equations with singularity. By using implicit rules and composite numerical quadrature rules, scheme established on a Shishkin mesh. The stability convergence proposed are analyzed two examples solved display advantages presented technique.

*Correspondence: [email protected] 2Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia Full list of author information is available at the end of the article Abstract In this paper, we derive a new generalized Volterra–Fredholm integral inequality and use it to study the dependence of solutions on the ini...

Abstract The main goal of this paper is to obtain error bounds for parabolic integro-differential equation. derivation these based elliptic and Ritz -Volterra reconstructions introduced by Makridakis Nochetto 2003 then extended - Volterra reconstruction in case integro-parabolic differential problems Reddy Sinha 2015. We proved optimal order certain classes semilinear intergro equations. key po...

A numerical scheme, based on the cubic B-spline wavelets for solving fractional integro-differential equations is presented. The fractional derivative of these wavelets are utilized to reduce the fractional integro-differential equation to system of algebraic equations. Numerical examples are provided to demonstrate the accuracy and efficiency and simplicity of the method.

This paper presents a computational technique for solving linear and nonlinear Fredholm integro-differential equations of fractional order. In addition, examples that illustrate the pertinent features of this method are presented, and the results of the study are discussed. Results have revealed that the RKHSM yields efficiently a good approximation to the exact solution.

Abstract In this article, first, we present an example of fuzzy normed space by means the Mittag-Leffler function. Next, extend concept to matrix valued and also introduce a class control functions stabilize nonlinear ϕ -Hadamard fractional Volterra integro-differential equation. sense, investigate Ulam–Hyers–Rassias stability for kind equations in Banach space. Finally, as application, using f...

In this work, the existence and uniqueness solution of fractional nonlinear mixed integro-differential equation (FrNMIoDE) is guaranteed with a general discontinuous kernel based on position time-space L2Ω×C0,T, T<1. The FrNMIoDE conformed to Volterra-Hammerstein integral (V-HIE) second kind, after applying characteristics integral, in for Hammerstein term continuous time Volterra (VI) term....