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A numerical scheme based on non-discretization of data for boundary value problems of fractional order differential equations

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this article, we develop a powerful method for the numerical solution of boundary value problems (BVPs) of fractional order differential equations (FDEs). Omitting the discretization of data by using Bernstein polynomials, we construct the required scheme. With the help of this scheme we convert the concerned FDEs to algebraic equations whose solutions led us to the numerical solution of the considered problem. Numerical examples are provided to illustrate our main results. Also comparison of the results with the exact solutions and other method like (Haar wavelets) is provided to justify the efficiency of the proposed scheme.

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Acknowledgements

We are really thankful to the reviewers for their useful suggestions which improved this paper very well.

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Authors and Affiliations

  1. Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan

    Kamal Shah

  2. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China

    JinRong Wang

  3. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China

    JinRong Wang

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  1. Kamal Shah
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Correspondence to Kamal Shah.

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This work was supported by the National Natural Science Foundation of China (11661016), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Science and Technology Program of Guizhou Province ([2017]5788), and Major Research Project of Innovative Group in Guizhou Education Department ([2018]012).

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Shah, K., Wang, J. A numerical scheme based on non-discretization of data for boundary value problems of fractional order differential equations. RACSAM 113, 2277–2294 (2019). https://doi.org/10.1007/s13398-018-0616-7

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