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

  • Kamal ShahEmail author
  • JinRong Wang
Original Paper
  • 41 Downloads

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.

Keywords

Fractional differential equations Boundary value problem Numerical solutions Bernstein polynomials Discretization of data 

Mathematics Subject Classifications

34L05 65L05 65T99 34G10 

Notes

Acknowledgements

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

Compliance with ethical standards

Competing interests

We declare that no competing interest exist regarding this paper.

Authors contribution

All authors equally contributed this paper.

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Copyright information

© The Royal Academy of Sciences, Madrid 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MalakandKhyber PakhtunkhwaPakistan
  2. 2.Department of MathematicsGuizhou UniversityGuiyangChina
  3. 3.School of Mathematical SciencesQufu Normal UniversityQufuChina

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