On a Boundary-Initial Value Problem for Fractional Differential Equation with Sequential Caputo derivatives
Provides analytic and numerical solutions for a specific class of fractional differential equations, but the approach is incremental as it extends known techniques to a new equation type.
The paper derives the exact analytic solution for a fractional differential equation with sequential Caputo derivatives using the bivariate Mittag-Leffler function and develops a numerical scheme via L1-finite element method.
In this paper, we investigate a fractional differential equation involving sequential Caputo derivatives, motivated by recent research on fractional models with multiple memory effects. Using techniques inspired by earlier works on sequential fractional operators, we derive the exact analytic solution of the problem in terms of the bivariate Mittag-Leffler function. Additionally, several useful properties of the bivariate Mittag-Leffler function are formulated to support the solution construction. Furthermore, we develop a numerical scheme using a sequential reformulation and the L1-finite element method.