A $\star$-Product Approach for Analytical and Numerical Solutions of Nonautonomous Linear Fractional Differential Equations
For researchers working on fractional differential equations, this provides a novel framework that may simplify solving certain classes of problems, though the practical impact is not quantified.
The paper introduces a new solution method for nonautonomous linear fractional differential equations using the $\star$-product, enabling both analytical and numerical solutions. The approach yields closed-form solutions in certain cases.
This article presents a novel solution method for nonautonomous linear ordinary fractional differential equations. The approach is based on reformulating the analytical solution using the $\star$-product, a generalization of the Volterra convolution, followed by an appropriate discretization of the resulting expression. Additionally, we demonstrate that, in certain cases, the $\star$-formalism enables the derivation of closed-form solutions, further highlighting the utility of this framework.