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Wavelet Methods for Solving Fractional Order Differential Equations

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  • A. K. Gupta
  • S. Saha Ray

Abstract

Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and many more. In this paper, we review different wavelet methods for solving both linear and nonlinear fractional differential equations. Our goal is to analyze the selected wavelet methods and assess their accuracy and efficiency with regard to solving fractional differential equations. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study on various wavelets in order to solve differential equations of arbitrary order.

Suggested Citation

  • A. K. Gupta & S. Saha Ray, 2014. "Wavelet Methods for Solving Fractional Order Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-11, May.
    • Handle: RePEc:hin:jnlmpe:140453
    DOI: 10.1155/2014/140453
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    Cited by:

    1. Haifa Bin Jebreen, 2024. "A Highly Accurate Computational Approach to Solving the Diffusion Equation of a Fractional Order," Mathematics, MDPI, vol. 12(13), pages 1-15, June.

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