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arXiv 2008.063062020-08-14math.DS

On the Nonlinear $Ψ$-Hilfer Hybrid Fractional Differential Equations

Kishor D. Kucche, Ashwini D. Mali

备注：: 24
DOI：: 10.1016/j.chaos.2021.111335

英文摘要：

In this paper, we initially derive the equivalent fractional integral equation to $Ψ$-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 $Ψ$-Hilfer derivative and utilize it to derive the hybrid fractional differential inequalities involving $Ψ$-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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