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Applying the Reproducing Kernel Method to Fractional Differential Equations with Periodic Conditions in Hilbert Space

Author

Listed:
  • Hoda Saky
  • Saeid Abbasbandy
  • Elyas Shivanian

Abstract

In this article, the reproducing kernel method is presented for the fractional differential equations with periodic conditions in the Hilbert space. This method gives an approximate solution to the problem. The approximate and exact solutions are displayed in the form of series in the reproduction kernel space. In addition, we provide an error analysis for this technique. The presented method is tested by some examples to show its precision.

Suggested Citation

  • Hoda Saky & Saeid Abbasbandy & Elyas Shivanian, 2022. "Applying the Reproducing Kernel Method to Fractional Differential Equations with Periodic Conditions in Hilbert Space," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:6261378
    DOI: 10.1155/2022/6261378
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    References listed on IDEAS

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    1. Baleanu, D. & Shiri, B., 2018. "Collocation methods for fractional differential equations involving non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 136-145.
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    3. Saad, Khaled M. & Srivastava, H.M. & Gómez-Aguilar, J.F., 2020. "A Fractional Quadratic autocatalysis associated with chemical clock reactions involving linear inhibition," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
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