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arXiv · 2008.06306

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

Kishor D. Kucche·Ashwini D. Mali
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Abstract

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.

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Kishor D. Kucche, Ashwini D. Mali. 2020-08-14. On the Nonlinear $\Psi$-Hilfer Hybrid Fractional Differential Equations. https://doi.org/10.1016/j.chaos.2021.111335

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