On stability analysis of hybrid fractional boundary value problem

Vidushi Gupta (), Arshad Ali (), Kamal Shah () and Syed Abbas ()
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Vidushi Gupta: Chandigarh University
Arshad Ali: University of Malakand
Kamal Shah: University of Malakand
Syed Abbas: Indian Institute of Technology Mandi

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 1, 27-38

Abstract: Abstract The novelty of the present article is to introduce the study of hybrid dynamical system of order $$\xi \in (\delta -1,\delta ]$$ ξ ∈ ( δ - 1 , δ ] with finite time delay. These hybrid systems are more suitable to deal several dynamical process as particular cases. The importance of this manuscript is to discuss the concept of stability results including Ulam-Hyers stability (UHS), generalized Ulam-Hyers stability (GUHS), Ulam-Hyers Rassias stability (UHRS) and generalized Ulam-Hyers Rassias stability (GUHRS). Meanwhile, we investigate some sufficient conditions for existence result of the solution for proposed work by adopting the application of fixed point theorem of Banach algebra due to Dhage under mixed Lipschitz and Carathéodory conditions. Finally the paper is enriched by two interesting applications to demonstrate our results.

Keywords: Nonlocal conditions; Hybrid differential equation; Fractional order differential equation; Hybrid fixed point theorem; 26A33; 34K05; 34A12 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00133-5

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