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Article

Existence Results for Hilfer Fractional Differential Equations with Variable Coefficient

School of Mathematics, Yunnan Normal University, Kunming 650092, China
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Academic Editor: Paul Eloe
Fractal Fract. 2022, 6(1), 11; https://doi.org/10.3390/fractalfract6010011
Received: 16 November 2021 / Revised: 11 December 2021 / Accepted: 22 December 2021 / Published: 28 December 2021
The aim of this paper is to establish the existence and uniqueness results for differential equations of Hilfer-type fractional order with variable coefficient. Firstly, we establish the equivalent Volterra integral equation to an initial value problem for a class of nonlinear fractional differential equations involving Hilfer fractional derivative. Secondly, we obtain the existence and uniqueness results for a class of Hilfer fractional differential equations with variable coefficient. We verify our results by providing two examples. View Full-Text
Keywords: fractional differential equation; Hilfer fractional derivative; variable coefficient fractional differential equation; Hilfer fractional derivative; variable coefficient
MDPI and ACS Style

Li, F.; Wang, C.; Wang, H. Existence Results for Hilfer Fractional Differential Equations with Variable Coefficient. Fractal Fract. 2022, 6, 11. https://doi.org/10.3390/fractalfract6010011

AMA Style

Li F, Wang C, Wang H. Existence Results for Hilfer Fractional Differential Equations with Variable Coefficient. Fractal and Fractional. 2022; 6(1):11. https://doi.org/10.3390/fractalfract6010011

Chicago/Turabian Style

Li, Fang, Chenglong Wang, and Huiwen Wang. 2022. "Existence Results for Hilfer Fractional Differential Equations with Variable Coefficient" Fractal and Fractional 6, no. 1: 11. https://doi.org/10.3390/fractalfract6010011

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