"Solvability and Controllability of a Retarded-Type Nonlocal Non-Autono" by Madhukant Sharma and Shruti Dubey
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Progress in Fractional Differentiation & Applications

Author Country (or Countries)

India

Abstract

This paper considers a non-autonomous retarded-type fractional differential equation involving Caputo derivative along with a nonlocal condition in a general Banach space. We present a novel approach to determine the existence-uniqueness and controllability of mild solution to the considered problem using the fixed-point technique, classical semigroup theory, and tools of fractional calculus. It is imperative to mention that the main results are established without assuming the continuity of linear operator −A(t) and compactness condition on semigroup. At the end, the developed theoretical results have been applied to a nonlocal fractional order retarded elliptic evolution equation.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/090310

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