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Abdelkrim Salim, Mouffak Benchohra, Existence and Ulam stability results of tempered ($\kappa, \psi$)-Hilfer fractional terminal differential problems, Eur. J. Math. Appl. 4 (2024), Article ID 19.

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Volume 4 (2024), Article ID 19

https://doi.org/10.28919/ejma.2024.4.19

Published: 24/09/2024

Abstract:

The main objective of this paper is to investigate several aspects including the existence, uniqueness, and ${\kappa}$-Mittag-Leffler-Ulam-Hyers stability of a specific class of terminal value problems. These problems involve implicit nonlinear fractional differential equations and tempered $({\kappa},\psi)$-Hilfer fractional derivatives. To accomplish this, we employ several mathematical tools. These include the fixed point theorem of Banach, Schauder’s fixed point theorem, and a generalization of the well-known Gronwall inequality. Additionally, we provide illustrative examples to demonstrate the practical effectiveness of our main findings.

How to Cite:

Abdelkrim Salim, Mouffak Benchohra, Existence and Ulam stability results of tempered ($\kappa, \psi$)-Hilfer fractional terminal differential problems, Eur. J. Math. Appl. 4 (2024), Article ID 19. https://doi.org/10.28919/ejma.2024.4.19