Effective Method for Solving Higher-Order Fractional Differential Equations Using Spline Functions (Contemporary Mathematics, 2024)
In this paper, appropriate spline functions in polynomial form are outlined and applied to solve higher-order linear fractional differential equations (H-OLFDEs). Several techniques have been proposed to solve this type of equations. A description of the projected methodology is first introduced. The method involves transforming the H-OLFDE of order α, with given initial conditions, into a system of fractional differential equations with , denoting the order of the Caputo fractional derivative for each equation i in the transformed system, where the number of equations in the resulting system is equal to that of initial conditions. The numerical results obtained using this strategy demonstrate substantial agreement with the precise analytical solutions. The results in this paper affirm the robustness and ease of application of the proposed technique.
Keywords: fractional differential equation; riemann-lioville fractional integral; caputo fractional derivative; spline functions; systems