An Accurate Approach to Simulate the Fractional Delay Differential Equations
Mohamed Adel, M. M. Khader, Salman Algelany, Khaled Aldwoah
Abstract
The fractional Legendre polynomials (FLPs) that we present as an effective method for solving fractional delay differential equations (FDDEs) are used in this work. The Liouville–Caputo sense is used to characterize fractional derivatives. This method uses the spectral collocation technique based on FLPs. The proposed method converts FDDEs into a set of algebraic equations. We lay out a study of the convergence analysis and figure out the upper bound on error for the approximate solution. Examples are provided to demonstrate the precision of the suggested approach.
Topics & Concepts
Legendre polynomialsConvergence (economics)Collocation (remote sensing)MathematicsAlgebraic equationCollocation methodFractional calculusSet (abstract data type)Applied mathematicsDifferential equationUpper and lower boundsAssociated Legendre polynomialsSpectral methodDifferential (mechanical device)Mathematical analysisOrthogonal polynomialsComputer scienceNonlinear systemOrdinary differential equationClassical orthogonal polynomialsPhysicsGegenbauer polynomialsEconomic growthQuantum mechanicsEconomicsMachine learningProgramming languageThermodynamicsFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsIterative Methods for Nonlinear Equations