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Cubo (Temuco)
versión On-line ISSN 0719-0646
Cubo vol.24 no.2 Temuco ago. 2022
http://dx.doi.org/10.56754/0719-0646.2402.0273
Articles
On existence results for hybrid ψ−Caputo multi-fractional differential equations with hybrid conditions
1Mathematics and Applied Sciences Laboratory, Ghardaia University, Ghardaia 47000, Algeria. fouadfredj05@gmail.com fredj.fouad@univ-ghardaia.dz
2Mathematics and Applied Sciences Laboratory, Ghardaia University, Ghardaia 47000, Algeria. h.hammouche@yahoo.fr
In this paper, we study the existence and uniqueness results of a fractional hybrid boundary value problem with multi-ple fractional derivatives of ψ −Caputo with different orders. Using a useful generalization of Krasnoselskii’s fixed point theorem, we have established results of at least one solution, while the uniqueness of solution is derived by Banach’s fixed point. The last section is devoted to an example that illustrates the applicability of our results.
Keywords and Phrases: −fractional derivative; fractional differential equation; hybrid conditions; fixed point; existence; uniqueness
En este artículo, estudiamos los resultados de existencia y unicidad de un problema de valor en la frontera fraccional híbrido con múltiples derivadas fraccionarias de ψ -Caputo con diferentes órdenes. Usando una generalización útil del teorema del punto fijo de Krasnoselskii, establecemos resultados de al menos una solución, mientras que la unicidad de dicha solución se obtiene a partir del punto fijo de Banach. La última sección está dedicada a un ejemplo que ilustra la aplicabilidad de nuestros resultados.
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Accepted: May 24, 2022; Received: October 14, 2021
This is an open-access article distributed under the terms of the Creative Commons Attribution License
