Qualitative Analysis of Coupled Fractional Differential Equations involving Hilfer Derivative

Abstract

In this manuscript, we have studied the coupled system of Hilfer fractional differential equations with non-local conditions. We have used the Leray-alternative Schauder’s and the Contraction principle to obtain the results on the existence and uniqueness of the solution of the proposed problem in the weighted space of continuous functions. For the defined problem, sufficient conditions have also been developed to determine the Ulam stability of the solution. The key conclusions are well-illustrated with examples.

Keywords

• fractional differential equations
• couple system
• hilfer fractional derivative
• non-local conditions
• fixed point theorem
• ulam’s stability
• primary 39b72, 39b52
• secondary 47h10