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We consider the following fractional-order differential equation investigate the existence of a unique solution and the Gauss Hypergeometric stability of this fractional-order differential equation (for more detail we refer to [1, 10, 17, 20, 22, 23, 26]). In the above equation, \(^c{D}_\jmath ^{\alpha }\) for a function \(\rho \) given on the interval \(J=(0,q],~~ q{\in }\mathbb {R}_+\) is the Caputo fractional derivative of order \(\alpha \) and the functions \(k \in C(J \times \mathbb {R}^2,\mathbb {R}),~~ h \in C(\bar{J},\bar{J})\) ( \(\bar{J}\) is the colure of J) with \(h(\jmath ) \le \jmath \) . In the first theorem, we investigate the Gauss Hypergeometric stability of the fractional-order differential equation using the Chebyshev norm and in the second theorem, we have proved the Gauss Hypergeometric stability of the equation by using Bielecki norm.

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Picard Method

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  • 发表日期：

    2025年

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  • Zahra Eidinejad,
  • Reza Saadati,
  • Tofigh Allahviranloo,
  • Chenkuan Li,
  • Javad Vahidi

摘要

We consider the following fractional-order differential equation investigate the existence of a unique solution and the Gauss Hypergeometric stability of this fractional-order differential equation (for more detail we refer to [1, 10, 17, 20, 22, 23, 26]). In the above equation, \(^c{D}_\jmath ^{\alpha }\) for a function \(\rho \) given on the interval \(J=(0,q],~~ q{\in }\mathbb {R}_+\) is the Caputo fractional derivative of order \(\alpha \) and the functions \(k \in C(J \times \mathbb {R}^2,\mathbb {R}),~~ h \in C(\bar{J},\bar{J})\) ( \(\bar{J}\) is the colure of J) with \(h(\jmath ) \le \jmath \) . In the first theorem, we investigate the Gauss Hypergeometric stability of the fractional-order differential equation using the Chebyshev norm and in the second theorem, we have proved the Gauss Hypergeometric stability of the equation by using Bielecki norm.