Analytic Solutions of (N+1) Dimensional Time Fractional Diffusion Equations by Fractional Iterative Laplace Transform Method

Kebede Shigute Kenea

Analytic Solutions of (N+1) Dimensional Time Fractional Diffusion Equations by Fractional Iterative Laplace Transform Method

Kebede Shigute Kenea * §

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§ Jimma College of Teacher Education

Analytic Solutions of (N+1) Dimensional Time Fractional Diffusion Equations by Fractional Iterative Laplace Transform Method

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Abstract

In this paper, the author has been examined how to obtain solutions of (n+1) dimensional time fractional diffusion equations with initial conditions in the form of infinite fractional power series, in terms of Mittage Lefler function of one parameter and exact form by the use of iterative fractional Laplace transform method (IFLTM). The basic idea of the IFLTM was developed successfully. To see its effectiveness and applicability, three test examples were presented. The closed solutions in the form of infinite fractional power series and in terms of Mittag-Leffler functions in one parameter, which rapidly converge to exact solutions, were successfully derived analytically by the use of iterative fractional Laplace transform method (IFLTM). Thus, the results show that the iterative fractional Laplace transform method works successfully in solving (n+1) dimensional time fractional diffusion equations in a direct way without using linearization, perturbation, discretization or restrictive assumptions, and hence it can be extended to other fractional differential equations.

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No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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How to Cite This Article

Kebede Shigute Kenea. 2018. "Analytic Solutions of (N+1) Dimensional Time Fractional Diffusion Equations by Fractional Iterative Laplace Transform Method". Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 18 (GJSFR Volume 18 Issue F4).

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GJSFR Volume 18 Issue F4

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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Classification

GJSFR-F Classification MSC 2010: 35J05

Submission ReceivedApril 5, 2018
Peer Review Double Blind
Handling Editor
Accepted May 1, 2018
Published May 14, 2018

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v1.2

Issue date

June 7, 2018

Language

English

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Total Score: 115

Country: Ethiopia

Subject: Global Journal of Science Frontier Research

Authors: Kebede Shigute Kenea (PhD/Dr. count: 0)

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