Existence Solution and Controllability of Sobolev Type Delay Nonlinear Fractional Integro-Differential System

Abstract

Fractional integro-differential equations arise in the mathematical modeling of various physical phenomena like heat conduction in materials with memory, diffusion processes, etc. In this manuscript, we prove the existence of mild solution for Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2. We establish the sufficient conditions for the approximate controllability of Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2. In addition, we prove the exact null controllability of Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2. Finally, an example is given to illustrate the obtained results.

New class of volterra integro-differential equations with fractal-fractional operators: Existence, uniqueness and numerical scheme

“…Integro-differential equations are equations which involve both integral and differential operators. In this aspect, these equations have become more interesting in creating new ideas in the last years [[11]- [4]]. Volterra integro-differential equations which are an important class of these equations have arise widely in the mathematical modelling of many physical and biological processes, for example biological species coexisting together with increasing and decreasing rate of growth, electromagnetic theory, Wilson-Cowan model and many more [15].…”