A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model
Muhammad Sarmad Arshad, Dumitru Bǎleanu, Muhammad Bilal Riaz, Muhammad Abbas
Abstract
In this paper, the fractional Euler method has been studied, and the derivation of the novel 2-stage fractional Runge–Kutta (FRK) method has been presented. The proposed fractional numerical method has been implemented to find the solution of fractional differential equations. The proposed novel method will be helpful to derive the higher-order family of fractional Runge–Kutta methods. The nonlinear fractional Logistic Growth Model is solved and analyzed. The numerical results and graphs of the examples demonstrate the effectiveness of the method.
Topics & Concepts
Fractional calculusRunge–Kutta methodsLogistic functionMathematicsNonlinear systemApplied mathematicsEuler's formulaStage (stratigraphy)Order (exchange)Fractional programmingStability (learning theory)Differential equationMathematical analysisComputer sciencePhysicsStatisticsNonlinear programmingPaleontologyBiologyQuantum mechanicsMachine learningEconomicsFinanceFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsIterative Methods for Nonlinear Equations