Existence Results for Hilfer Fractional Differential Equations with Variable Coefficient

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 differentia...

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Bibliographic Details
Published in:Fractal and fractional 2022-01, Vol.6 (1), p.11
Main Authors: Li, Fang, Wang, Chenglong, Wang, Huiwen
Format: Article
Language:English
Subjects:
Banach spaces
Boundary value problems
Coefficients
Differential equations
fractional differential equation
Hilfer fractional derivative
Integral equations
Mathematical analysis
Uniqueness
variable coefficient
Volterra integral equations
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Summary: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.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract6010011