Abstract
In the current manuscript, we investigate existence of solutions to a coupled system of fractional hybrid differential equations (FHDEs). With the help of mixed type Lipschitz and Caratheodory conditions, some conditions for the existence of solutions to the considered problem are established. Considering the tools of nonlinear analysis and hybrid fixed points theory, we establish our results. Further some new type results about stability including Ulam-Hyers (UH), generalized Ulam-Hyers (GUH) stability, Ulam-Hyers-Rassias (UHR) and generalized Ulam-Hyers-Rassias (GUHR) stability are developed. A test problem is given to demonstrate the establish results.
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Acknowledgement
We thank the anonymous referees for their careful reading and suggestions which improved this paper very well. This research work has been supported financially by HED under grant No. HEREF-46 and HEC of Pakistan under grant No. NRPU-10039.
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Samina, Shah, K. & Khan, R.A. Stability theory to a coupled system of nonlinear fractional hybrid differential equations. Indian J Pure Appl Math 51, 669–687 (2020). https://doi.org/10.1007/s13226-020-0423-7
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DOI: https://doi.org/10.1007/s13226-020-0423-7