On nonlinear mixed fractional integro-differential equations with positive constant coefficient

‎Numerical solution of nonlinear fractional Volterra-Fredholm integro-differential equations with mixed boundary ‎conditions‎

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demo...

Nonlinear Integro - Differential Equations

Integro-differential Equations with Nonlinear Directional Dependence

We prove Hölder regularity results for a class of nonlinear elliptic integro-differential operators with integration kernels whose ellipticity bounds are strongly directionally dependent. These results extend those in [9] and are also uniform as the order of operators approaches 2.

On fractional integro-differential equations with state-dependent delay

In this article, we deal with the existence of mild solutions for a class of fractional integro-differential equations with state-dependent delay. Our results are based on the technique of measures of noncompactness and Darbo’s fixed point theorem. An example is provided to illustrate the main result. AMS Subject Classifications: 26A33, 34A08, 34A37, 34G20, 34G25, 34H05, 34K09, 34K30.

A Numerical Scheme for Solving Nonlinear Fractional Volterra Integro-Differential Equations

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....