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A Reproducing Kernel Hilbert Space Method for Solving Integro-Differential Equations of Fractional Order

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Abstract

In this article, we implement a relatively new analytical technique, the reproducing kernel Hilbert space method (RKHSM), for solving integro-differential equations of fractional order. The solution obtained by using the method takes the form of a convergent series with easily computable components. Two numerical examples are studied to demonstrate the accuracy of the present method. The present work shows the validity and great potential of the reproducing kernel Hilbert space method for solving linear and nonlinear integro-differential equations of fractional order.

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Authors and Affiliations

  1. Department of Science, Princess Sumaya University for Technology, Amman, 11941, Jordan

    Samia Bushnaq

  2. Faculty of Science, Department of Mathematics, The University of Jordan, Amman, 1194, Jordan

    Shaher Momani

  3. Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, 411105, China

    Yong Zhou

Authors
  1. Samia Bushnaq
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  2. Shaher Momani
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  3. Yong Zhou
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Correspondence to Shaher Momani.

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Bushnaq, S., Momani, S. & Zhou, Y. A Reproducing Kernel Hilbert Space Method for Solving Integro-Differential Equations of Fractional Order. J Optim Theory Appl 156, 96–105 (2013). https://doi.org/10.1007/s10957-012-0207-2

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  • DOI: https://doi.org/10.1007/s10957-012-0207-2

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