Version 1
: Received: 12 September 2024 / Approved: 12 September 2024 / Online: 12 September 2024 (11:35:54 CEST)
How to cite:
He, W.; Jin, Y.; Wang, L.; Mu, J. Existence and Stability for Fractional Differential Equations with a Regularized ψ–Hilfer Fractional Derivative. Preprints2024, 2024090991. https://doi.org/10.20944/preprints202409.0991.v1
He, W.; Jin, Y.; Wang, L.; Mu, J. Existence and Stability for Fractional Differential Equations with a Regularized ψ–Hilfer Fractional Derivative. Preprints 2024, 2024090991. https://doi.org/10.20944/preprints202409.0991.v1
He, W.; Jin, Y.; Wang, L.; Mu, J. Existence and Stability for Fractional Differential Equations with a Regularized ψ–Hilfer Fractional Derivative. Preprints2024, 2024090991. https://doi.org/10.20944/preprints202409.0991.v1
APA Style
He, W., Jin, Y., Wang, L., & Mu, J. (2024). Existence and Stability for Fractional Differential Equations with a Regularized ψ–Hilfer Fractional Derivative. Preprints. https://doi.org/10.20944/preprints202409.0991.v1
Chicago/Turabian Style
He, W., Luyao Wang and Jia Mu. 2024 "Existence and Stability for Fractional Differential Equations with a Regularized ψ–Hilfer Fractional Derivative" Preprints. https://doi.org/10.20944/preprints202409.0991.v1
Abstract
This article aims to explore the existence and stability of solutions to differential equations involving a regularized ψ−Hilfer fractional derivative, which, compared to standard ψ−Hilfer fractional derivatives, provide a clear physical interpretation when dealing with initial conditions. We discovered that the regularized ψ−Hilfer fractional derivative can be represented as the inverse operation of the ψ−Riemann–Liouville fractional integral, and used this property to prove the existence of solutions for linear differential equations with a regularized ψ−Hilfer fractional derivative. Additionally, we applied the Mönch’s fixed-point theorem and knowledge of non-compactness measures to demonstrate the existence of solutions for nonlinear differential equations with a regularized ψ−Hilfer fractional derivative, and further discussed Ulam-Hyers-Rassias stability and semi-Ulam-Hyers-Rassias stability of these solutions. Finally, we illustrated our results through case studies.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
