This paper presents a novel numerical method for solving nonlinear fractional delay differential equations. Our approach uses fractional Jacobi functions in conjunction with a straightforward Picard iteration scheme to construct numerical solutions. Unlike some existing techniques, the proposed method is computationally efficient and avoids complex calculations. The use of orthogonal functions within the Picard iterations provides accurate approximations. Also, a convergence analysis demonstrates the method's high accuracy. We demonstrate the method's applicability and effectiveness by solving several challenging fractional delay differential equations, including the fractional pantograph equation and the fractional Hutchinson model. The results confirm that our method performs better than other numerical methods.
Ansari, S. and Akrami, M. H. (2026). Numerical Solution of Nonlinear Fractional Delay Differential Equations Using Fractional Jacobi Functions and Picard Iteration. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2026.67629.3230
MLA
Ansari, S. , and Akrami, M. H. . "Numerical Solution of Nonlinear Fractional Delay Differential Equations Using Fractional Jacobi Functions and Picard Iteration", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2026.67629.3230
HARVARD
Ansari, S., Akrami, M. H. (2026). 'Numerical Solution of Nonlinear Fractional Delay Differential Equations Using Fractional Jacobi Functions and Picard Iteration', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2026.67629.3230
CHICAGO
S. Ansari and M. H. Akrami, "Numerical Solution of Nonlinear Fractional Delay Differential Equations Using Fractional Jacobi Functions and Picard Iteration," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2026.67629.3230
VANCOUVER
Ansari, S., Akrami, M. H. Numerical Solution of Nonlinear Fractional Delay Differential Equations Using Fractional Jacobi Functions and Picard Iteration. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2026.67629.3230
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