Solution of Nonlinear Fractional Differential Equation using Picard’s Iteration Method with Integrating Factor Approach

This study investigates the resolution of non-linear differential equations of non-integer order by utilizing Picard's Iteration Method in conjunction with the Integrating Factor technique. Numerical examples are solved to showcase the precision of the proposed method. The approach is simple and particularly well-suited for tackling nonlinear fractional order issues, providing an easier option compared to other semi-analytic techniques. Importantly, it eliminates the requirement to compute generic Lagrange multipliers or Adomian polynomials. This method can also be applied to nonlinear systems of fractional differential equations for additional problem-solving scenarios.

1]Acharya, F., Bhesaniya, K., Panchal J., (2023) Estimating Approximate Solutions of Non-Linear Caputo Fractional Differential Equations with Forcing Functions Using Picard's Iteration Method. Tuijin Jishu/Journal of Propulsion Technology ISSN: 1001-4055 vol. 44 No. 04 (2023). 2]Acharya, F., Bhesaniya, K., Panchal, J., (2022) Numerical Solution of COVID -19 model of Fractional order showing impact of Immunity Booster. Bull. Env. Pharmacol. Life Sci., vol. 11[2]:69-79. 3]Aisha F., Fareed Mourad S., Semary Hany N., Hassan, (2021) An approximate solution of fractional order Riccati equations based on controlled Picard’s method with Atangana–Baleanu fractional derivative. Alexandria Engineering Journal, vol. 61, Issue 5:3673-3678. 4]Ali , E., Ziada, A., (2021) Solution of Nonlinear Fractional Differential Equations Using Adomain Decomposition Method. International Journal of Systems Science and Applied Mathematics. vol. 6:  111-119. doi: 10.11648/j.ijssam.20210604.11. 5]Chandel, R.S., Singh, A. and Chouhan, D., (2017) Numerical Solution of Fractional Order Differential Equations Using Haar Wavelet Operational Matrix. Palestine Journal of Mathematics, vol. 6: 515-3523. 6]Daraghmeh, A., Qatanani, N. and Saadeh, A. (2020) Numerical Solution of Fractional Differential Equations. Applied Mathematics, vol. 11: 1100-1115. 7]Das, S. and Gupta, P.K., (2011) Homotopy Analysis Method for Solving Fractional Hyperbolic Partial Differential Equations. International Journal of Computer Mathematics, vol. 88:578-588. 8]Elsaid, A., (2011) Homotopy Analysis Method for Solving a Class of Fractional Partial Differential Equations. Communications in Nonlinear Science and Numerical Simulation, vol. 16:3655-3664. 9]Ilejimi D.O, 2Okai J.O and Raheem R., L., (2019) On The Numerical Solution of Picard Iteration Method for Fractional Integro - Differential Equation. International Journal of Scie ntific and Research Publications, vol. 9, Issue 3: 8757. 10]Jafari, H., Daftardar-Gejji, V., (2006) Solving a system of nonlinear fractional differential equations using Adomian decomposition. Journal of Computational and Applied Mathematics, vol. 196(2): 644–651.