On the Nonlinear $\Psi$-Hilfer Hybrid Fractional Differential Equations

By Kishor D. Kucche, Ashwini D. Mali. 2020

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In this paper, we initially derive the equivalent fractional integral equation to $\Psi$-Hilfer hybrid fractional differential equations and through it, we prove the existence of a solution in the weighted space. The primary objective of the paper is to obtain estimates on $\Psi$-Hilfer derivative and utilize it to derive the hybrid fractional differential inequalities involving $\Psi$-Hilfer derivative. With the assistance of these fractional differential inequalities, we determine the existence of extremal solutions, comparison theorems and uniqueness of the solution.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/dee28d3d4aff8ee7810716c3140aea1653476a8b