Existence Results for Hilfer Fractional Differential Equations with Variable Coefficient
Fang Li, Chenglong Wang, Huiwen Wang
Abstract
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.
Topics & Concepts
MathematicsUniquenessVariable (mathematics)Nonlinear systemDifferential equationMathematical analysisFractional calculusClass (philosophy)Applied mathematicsPhysicsComputer scienceArtificial intelligenceQuantum mechanicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods