New interpretation of topological degree method of Hilfer fractional neutral functional integro-differential equation with nonlocal condition

Abstract

This manuscript deals with the concept of Hilfer fractional neutral functional integro-differential equation with a nonlocal condition. The solution representation of a given system is obtained from the strongly continuous operator, linear operator and bounded operator, as well as the Wright type of function. The sufficient and necessary conditions for the existence of a solution are attained using the topological degree method. The uniqueness of the solution is attained by Gronwall's inequality. Finally, we employed some specific numerical computations to examine the effectiveness of the results.

Keywords

• hilfer fractional derivative
• nonlocal condition
• kuratowski measure of non-compactness
• existence and uniqueness
• gronwall's inequality