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On stability analysis of hybrid fractional boundary value problem

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Abstract

The novelty of the present article is to introduce the study of hybrid dynamical system of order \(\xi \in (\delta -1,\delta ]\) 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.

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Acknowledgements

We are thankful to the reviewers for their careful reading and suggestions. Further we are thankful to HED and HEC of Pakistan for supporting this research under grant HEREF-46 and NRPU:10039 respectively.

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Authors and Affiliations

  1. Department of Mathematics, Chandigarh University, Chandigarh, Punjab, India

    Vidushi Gupta

  2. Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan

    Arshad Ali & Kamal Shah

  3. School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, India

    Syed Abbas

Authors
  1. Vidushi Gupta
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  2. Arshad Ali
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  3. Kamal Shah
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  4. Syed Abbas
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All authors have equal contribution in this work.

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Correspondence to Kamal Shah.

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Communicated by K Sandeep.

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Gupta, V., Ali, A., Shah, K. et al. On stability analysis of hybrid fractional boundary value problem. Indian J Pure Appl Math 52, 27–38 (2021). https://doi.org/10.1007/s13226-021-00133-5

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  • DOI: https://doi.org/10.1007/s13226-021-00133-5

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