On the existence and Ulam-Hyers stability for implicit fractional differential equation via fractional integral-type boundary conditions-Reference-Cited by-同舟云学术

On the existence and Ulam-Hyers stability for implicit fractional differential equation via fractional integral-type boundary conditions

Published:2024-01-01 Issue:1 Volume:57 Page:
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

El-Sayed Ahmed Mohamad¹,Al-Issa Shorouk Mahmoud²,El Miari Maysaa Mohamad³

Affiliation:

1. Department of mathematics, Faculty of Science, Alexandria University , Alexandria , Egypt

2. Department of Mathematics, Faculty of Science, Lebanese International University , Saida , Lebanon

3. Department of Mathematics, Faculty of Science, The International University of Beirut , Beirut , Lebanon

Abstract

Abstract This study investigates the existence of solutions for implicit fractional differential equations with fractional-order integral boundary conditions. We create the required conditions to ensure unique solution and Ulam-Hyers-Rassias stability. We also give examples to highlight the major findings.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/dema-2023-0130/pdf

Reference30 articles.

1. Sh. M. Al-Issa, A. M. A. El-Sayed, and H. H. G. Hashem, An outlook on hybrid fractional modeling of a heat controller with multi-valued feedback control, Fractal Fract. 7 (2023), no, 10, 759, DOI: https://doi.org/10.3390/fractalfract7100759.

2. S. M. Al-Issa, I. H. Kaddoura, and N. J. Rifai, Existence and Hyers-Ulam stability of solutions to the implicit second-order differential equation via fractional integral boundary conditions, J. Math. Computer Sci. 31 (2023), no. 1, 15–29.

3. A. M. A. El-Sayed and Sh. M Al-Issa, On a set-valued functional integral equation of Volterra-Stiltjes type, J. Math. Computer Sci. 21 (2020), no. 4, 273–285.

4. A. M. A. El-Sayed, H. H. G. Hashem and Sh. M Al-Issa, Analysis of a hybrid integro-differential inclusion, Bound. Value Probl. 2022 (2022), 68, DOI: https://doi.org/10.1186/s13661-022-01650-w.

5. I. Podlubny and A. M. A. EL-Sayed, On two definitions of fractional calculus, Preprint UEF 03-69 (ISBN 80-7099-252-2), Solvak Academy of Science-Institute of Experimental phys., 1996.