论文标题
在非线性$ψ$ hilfer混合分数微分方程
On the Nonlinear $Ψ$-Hilfer Hybrid Fractional Differential Equations
论文作者
论文摘要
在本文中，我们最初将等效的分数积分方程得出到$ψ$ - hilfer混合分数微分方程，并通过它证明了加权空间中解决方案的存在。本文的主要目的是获得对$ψ$ hilfer导数的估计，并利用它来推导涉及$ψ$ hilfer衍生物的混合分数差分不平等。在这些分数差异不平等的帮助下，我们确定了极端解，比较定理和溶液的唯一性的存在。
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.
