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A new family of predictor-corrector methods for solving fractional differential equations

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  • Kumar, Manoj
  • Daftardar-Gejji, Varsha

Abstract

In the present paper, we propose a new family of six predictor-corrector methods to solve non-linear fractional differential equations (FDEs) of the form Dαy(t)=f(t,y(t)),0<α<1, where Dα denotes the αth order Caputo derivative and perform the stability and error analysis. Further, we extend these methods for solving systems of FDEs. The proposed methods have higher order accuracy and their execution time is drastically reduced as compared to existing methods such as fractional Adams method (FAM) and new predictor-corrector method (NPCM). They require only 10% of the time taken by FAM and 20% of the NPCM. Further, these methods converge for very small values of α when FAM and NPCM fail. We illustrate the applicability of the proposed methods by solving a variety of examples and some chaotic systems.

Suggested Citation

  • Kumar, Manoj & Daftardar-Gejji, Varsha, 2019. "A new family of predictor-corrector methods for solving fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:363:y:2019:i:c:51
    DOI: 10.1016/j.amc.2019.124633
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    References listed on IDEAS

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    1. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
    2. Jhinga, Aman & Daftardar-Gejji, Varsha, 2018. "A new finite-difference predictor-corrector method for fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 418-432.
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    Cited by:

    1. Douaifia, Redouane & Bendoukha, Samir & Abdelmalek, Salem, 2021. "A Newton interpolation based predictor–corrector numerical method for fractional differential equations with an activator–inhibitor case study," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 391-413.
    2. Abdul-Aziz Hussein & Benyam Mebrate, 2025. "A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    3. Deng, Dingwen & Wu, Qiang, 2023. "Accuracy improvement of a Predictor–Corrector compact difference scheme for the system of two-dimensional coupled nonlinear wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 223-249.

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