APPROXIMATE CONTROLLABILITY OF IMPULSIVE FRACTIONAL INTEGRO-DIFFERENTIAL SYSTEMS WITH NONLOCAL CONDITIONS IN HILBERT SPACE

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 article, sufficient conditions are derived for approximate controllability of impulsive fractional integro-differential systems with nonlocal conditions in Hilbert space. The results are obtained by using fractional calculus, semigroup theory and the Darbo-Sadovskii's fixed point theorem. For an application, a specific type of ultraslow diffusion type of porous medium leading to the fractional partial integro-differential equation is demonstrated and numerical simulation is established to validate the derived theoretical results.