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Analytical Solutions of Fractional Order Diffusion Equations by Natural Transform Method

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Abstract

In this article, we develop an analytical method for solving fractional order partial differential equations. Our method is the generalizations of homotopy perturbations Laplace transform method and homotopy perturbations Sumudu transform method. The solutions obtained using the proposed method implies that the method is highly accurate and easy to implement. The proposed method can be easily applied to a large variety of problems, which are modeled in terms of fractional order partial differential equations. Some test problems are solved to show the accuracy of the proposed method. Some results are shown graphically also.

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Authors and Affiliations

  1. Department of Mathematics, University of Malakand, Chakadara Dir(L), Chakdara, Khyber Pakhtunkhwa, Pakistan

    Kamal Shah & Rahmat Ali Khan

  2. Department of Mathematics, University of Poonch Rawalakot, Rawalakot, AJK, Pakistan

    Hammad Khalil

Authors
  1. Kamal Shah
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  2. Hammad Khalil
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  3. Rahmat Ali Khan
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Correspondence to Kamal Shah.

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Shah, K., Khalil, H. & Khan, R.A. Analytical Solutions of Fractional Order Diffusion Equations by Natural Transform Method. Iran J Sci Technol Trans Sci 42, 1479–1490 (2018). https://doi.org/10.1007/s40995-016-0136-2

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  • DOI: https://doi.org/10.1007/s40995-016-0136-2

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