Eidinejad Zahra, Saadati Reza
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran.
Math Biosci Eng. 2022 Apr 25;19(7):6536-6550. doi: 10.3934/mbe.2022308.
In this paper, using the fractional integral with respect to the Ψ function and the Ψ-Hilfer fractional derivative, we consider the Volterra fractional equations. Considering the Gauss Hypergeometric function as a control function, we introduce the concept of the Hyers-Ulam-Rassias-Kummer stability of this fractional equations and study existence, uniqueness, and an approximation for two classes of fractional Volterra integro-differential and fractional Volterra integral. We apply the Cădariu-Radu method derived from the Diaz-Margolis alternative fixed point theorem. After proving each of the main theorems, we provide an applied example of each of the results obtained.
在本文中，利用关于Ψ函数的分数阶积分和Ψ - 希弗尔分数阶导数，我们考虑沃尔泰拉分数阶方程。将高斯超几何函数视为控制函数，我们引入此类分数阶方程的赫尔斯 - 乌拉姆 - 拉西亚斯 - 库默稳定性概念，并研究两类分数阶沃尔泰拉积分 - 微分方程和分数阶沃尔泰拉积分方程的存在性、唯一性及近似解。我们应用源自迪亚兹 - 马戈利斯择一定理的卡达留 - 拉杜方法。在证明每个主要定理后，我们给出所获各结果的一个应用实例。
