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A Study of Fractional Differential Equation with a Positive Constant Coefficient via Hilfer Fractional Derivative

Authors: 

Hoa Ngo Van, Vu Ho

Source title: 
Mathematical Problems in Engineering, 2020: 2749138, 2020 (ISI)
Academic year of acceptance: 
2020-2021
Abstract: 

The aim of the paper is to consider the existence and uniqueness of solution of the fractional differential equation with a positive constant coefficient under Hilfer fractional derivative by using the fixed-point theorem. We also prove the bounded and continuous dependence on the initial conditions of solution. Besides, Hyers–Ulam stability and Hyers–Ulam–Rassias stability are discussed. Finally, we provide an example to demonstrate our main results.