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Theory and applications of a more general form for fractional power series expansion

Author

Listed:
  • Jaradat, I.
  • Al-Dolat, M.
  • Al-Zoubi, K.
  • Alquran, M.

Abstract

The latent potentialities and applications of fractional calculus present a mathematical challenge to establish its theoretical framework. One of these challenges is to have a compact and self-contained fractional power series representation that has a wider application scope and allows studying analytical properties. In this letter, we introduce a new more general form of fractional power series expansion, based on the Caputo sense of fractional derivative, with corresponding convergence property. In order to show the functionality of the proposed expansion, we apply the corresponding iterative fractional power series scheme to solve several fractional (integro-)differential equations.

Suggested Citation

  • Jaradat, I. & Al-Dolat, M. & Al-Zoubi, K. & Alquran, M., 2018. "Theory and applications of a more general form for fractional power series expansion," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 107-110.
    • Handle: RePEc:eee:chsofr:v:108:y:2018:i:c:p:107-110
    DOI: 10.1016/j.chaos.2018.01.039
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    References listed on IDEAS

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    1. El-Nabulsi, Rami Ahmad, 2009. "Fractional Dirac operators and deformed field theory on Clifford algebra," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2614-2622.
    2. El-Ajou, Ahmad & Abu Arqub, Omar & Al-Smadi, Mohammed, 2015. "A general form of the generalized Taylor’s formula with some applications," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 851-859.
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