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The purpose of the chapter is exhibiting the numerical solution of the linear and non-linear differential equation of fractional order \(0 < \alpha < 1 \) by Fractional Runge Kutta (FRK) method of orders 2, 3 and 4. The error analysis of this FRK methods are also examined. The efficiency of these methods is illustrated through the examples of fractional differential equations (FDEs). Numerical results show that the FRK method of order 4 is efficient for solving FDE.

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An Algorithm for the Numerical Solution of Fractional Differential Equations Using the Fractional Runge Kutta Methods

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  • 发表日期：

    2025年

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  • S. Katrin Lydia,
  • T. Sathiyaraj

摘要

The purpose of the chapter is exhibiting the numerical solution of the linear and non-linear differential equation of fractional order \(0 < \alpha < 1 \) by Fractional Runge Kutta (FRK) method of orders 2, 3 and 4. The error analysis of this FRK methods are also examined. The efficiency of these methods is illustrated through the examples of fractional differential equations (FDEs). Numerical results show that the FRK method of order 4 is efficient for solving FDE.