Full Text: PDF
DOI: 10.23952/jnfa.2020.48
Received June 30, 2020; Accepted November 10, 2020; Published November 28, 2020
Abstract. In this paper, we study the Ulam-Hyers and the generalized Ulam-Hyers-Rassias stability for linear fractional differential equations with hybrid proportional-Caputo derivatives using the Laplace transform method. The existence and uniqueness of solutions for nonlinear fractional differential equations with hybrid proportional-Caputo derivatives are established by means of Schaefer’s fixed point theorem, Banach’s fixed point theorem and the generalized Gronwall’s inequality. Two examples are also given to illustrate the main results.
How to Cite this Article:
Mohamed I. Abbas, Existence results and the Ulam stability for fractional differential equations with hybrid proportional-Caputo derivatives, Journal of Nonlinear Functional Analysis, Vol. 2020 (2020), Article ID 48, pp. 1-14.