Representation of Solutions of Linear Homogeneous Caputo Fractional Differential Equations with Continuous Variable Coefficients

Abstract

We consider the canonical fundamental systems of solutions of linear homogeneous Caputo fractional differential equations with continuous variable coefficients. Here we gained a series-representation of the canonical fundamental system by coefficients of the considered equations and the representation of solution to initial value problems using the canonical fundamental system. According to our results, the canonical fundamental system of solutions to linear homogeneous differential equation with Caputo fractional derivatives and continuous variable coefficients has different representations according to the distributions of the lowest order of the fractional derivatives in the equation and the distance from the highest order to its adjacent order of the fractional derivatives in the equation.

22 pages

References in corpus (4)

• Explicit Representations of Green's Function for Linear Fractional Differential Operator with Variable Coefficients
• Existence and Uniqueness of the Solution to a Nonlinear Differential Equation with Caputo Fractional Derivative in the Space of Continuously Differentiable Functions
• Existence and Solution-representation of IVP for LFDE with Generalized Riemann-Liouville fractional derivatives and $n$ terms
• Spline Collocation Method for Nonlinear Multi-Term Fractional Differential Equation