A qualitative study on generalized Caputo fractional integro-differential equations
| Autor: | Wasfi Shatanawi, Mohammed D. Kassim, Saeed M. Ali, Thabet Abdeljawad, Mohammed S. Abdo |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Mathematics::Functional Analysis Algebra and Number Theory Partial differential equation Functional analysis Differential equation Applied Mathematics Banach space Fixed-point theorem Absolute continuity Babenko’s technique Fixed point approach Fractional differential equation Generalized fractional derivative Ordinary differential equation QA1-939 Uniqueness Analysis Mathematics |
| Zdroj: | Advances in Difference Equations, Vol 2021, Iss 1, Pp 1-18 (2021) |
| ISSN: | 1687-1847 |
| Popis: | The aim of this article is to discuss the uniqueness and Ulam–Hyers stability of solutions for a nonlinear fractional integro-differential equation involving a generalized Caputo fractional operator. The used fractional operator is generated by iterating a local integral of the form $(I_{a}^{\rho }f)(t)=\int _{a}^{t}f(s)s^{\rho -1}\,ds$ ( I a ρ f ) ( t ) = ∫ a t f ( s ) s ρ − 1 d s . Our reported results are obtained in the Banach space of absolutely continuous functions that rely on Babenko’s technique and Banach’s fixed point theorem. Besides, our main findings are illustrated by some examples. |
| Databáze: | OpenAIRE |
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