Existence and stability analysis to the sequential coupled hybrid system of fractional differential equations with two different fractional derivatives

Mohamed Houas; Jehad Alzabut; Mahammad Khuddush

doi:10.11121/ijocta.2023.1278

Authors

Mohamed Houas Laboratory FIMA, UDBKM, Khemis Miliana University, Algeria https://orcid.org/0000-0001-6256-0511
Jehad Alzabut Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia https://orcid.org/0000-0002-5262-1138
Mahammad Khuddush Department of Mathematics, Dr. Lankapalli Bullayya College of Engineering, Resapuvanipalem, Visakhapatnam, 530013, Andhra Pradesh, India https://orcid.org/0000-0002-1236-8334

DOI:

https://doi.org/10.11121/ijocta.2023.1278

Keywords:

Coupled systems, Hybrid differential equations, Boundary value problem, Fractional derivative, Ulam-Hyers stability

Abstract

In this paper, we discussed the existence, uniqueness and Ulam-type stability of solutions for sequential coupled hybrid fractional differential equations with two derivatives. The uniqueness of solutions is established by means of Banach's contraction mapping principle, while the existence of solutions is derived from Leray-Schauder's alternative fixed point theorem. Further, the Ulam-type stability of the addressed problem is studied. Finally, an example is provided to check the validity of our obtained results.

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Author Biographies

Mohamed Houas, Laboratory FIMA, UDBKM, Khemis Miliana University, Algeria

Mohamed Houas is working as an assistant professor at Universite Djilali BOUNAAMA Khemis Miliana, Algeria and his research interest are fractional differential equations and fractional integral inequalities.

Jehad Alzabut, Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia

Jehad Alzabut is working as a professor at Prince Sultan University, Saudi Arabia and his research interest are fractional differential equations, and dynamic equations on time scales.

Mahammad Khuddush, Department of Mathematics, Dr. Lankapalli Bullayya College of Engineering, Resapuvanipalem, Visakhapatnam, 530013, Andhra Pradesh, India

Mahammad Khuddush is working as an assistant professor at Dr. Lankapalli Bullayya College of Engineering, India and his research interest are fractional differential equations, dynamic equations on time scales, fixed point theory, neural networks, global existence and blow-up solutions of PDE.

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