A novel fractional Bernoulli-Picard iteration method to solve fractional differential equations

	A novel fractional Bernoulli-Picard iteration method to solve fractional differential equations
Journal of Mathematical Modeling
مقاله 21، دوره 13، شماره 1، خرداد 2025، صفحه 139-152 اصل مقاله (299.47 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2024.28329.2497
نویسندگان
Fatemeh Zakipour؛ Abbas Saadatmandi^*
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran
چکیده
This paper introduces a new computational method for solving linear and non-linear fractional differential equations (FDEs). Our method essentially consists of the combination of orthonormal Bernoulli polynomials and the fractional form of the Picard iteration method. We name this method the fractional Bernoulli-Picard iteration method (FBPIM). Unlike the spectral method, the proposed method does not require solving a set of algebraic equations. We also discuss the convergence of the method. Moreover, some numerical examples are included and compared with previously published results to assess both the accuracy and suitability of the developed technique.
کلیدواژه‌ها
Caputo derivative؛ Picard iteration method؛ Orthonormal Bernoulli polynomials؛ Fractional differential equations؛ Numerical solution

آمار تعداد مشاهده مقاله: 123 تعداد دریافت فایل اصل مقاله: 196

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