Abstract
In this paper, we study the existence and stability of Hilfer-type fractional differential equations (dynamic equations) on time scales. We obtain sufficient conditions for existence and uniqueness of solutions by using classical fixed point theorems such as Schauder’s fixed point theorem and Banach fixed point theorem. In addition, Ulam stability of the proposed problem is also discussed. As in application, we provide an example to illustrate our main results.
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Vivek, D., Kanagarajan, K. & Sivasundaram, S. On the Behavior of Solutions of Fractional Differential Equations on Time Scale Via Hilfer Fractional Derivatives. FCAA 21, 1120–1138 (2018). https://doi.org/10.1515/fca-2018-0060
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DOI: https://doi.org/10.1515/fca-2018-0060
Key Words and Phrases
- fractional differential equation
- time scales
- Hilfer fractional derivative
- existence
- Ulam stability
- fixed point