Closed Form Exact Solutions to the Higher Dimensional Fractional Schrodinger Equation via the Modified Simple Equation Method - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.1, January 2018

Journal of Applied Mathematics and Physics

Volume 6, Issue 1 (January 2018)

ISSN Print: 2327-4352 ISSN Online: 2327-4379

Google-based Impact Factor: 0.70 Citations

Closed Form Exact Solutions to the Higher Dimensional Fractional Schrodinger Equation via the Modified Simple Equation Method ()

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DOI: 10.4236/jamp.2018.61009 1,056 Downloads 2,328 Views Citations

Author(s)

M. Nurul Islam¹, M. Ali Akbar²

Affiliation(s)

¹Department of Mathematics, Islamic University, Kushtia, Bangladesh.
²Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh.

ABSTRACT

In this article, we investigate some exact wave solutions to the higher dimensional time-fractional Schrodinger equation, an important equation in quantum mechanics. The fractional Schrodinger equation further precisely describes the quantum state of a physical system changes in time. In order to determine the solutions a suitable transformation is considered to transmute the equations into a simpler ordinary differential equation (ODE) namely fractional complex transformation. We then use the modified simple equation (MSE) method to obtain new and further general exact wave solutions. The MSE method is more powerful and can be used in other works to establish completely new solutions for other kind of nonlinear fractional differential equations arising in mathematical physics. The affect of obtaining parameters for its definite values which are examined from the solutions of two dimensional and three dimensional time-fractional Schrodinger equations are discussed and therefore might be useful in different physical applications where the equations arise in this article.

KEYWORDS

Modified Simple Equation (MSE) Method, Fractional Differential Equation, Nonlinear Evolution Equations, Higher Dimensional Schrodinger Equation, Traveling Wave Transformation

Share and Cite:

Islam, M. and Akbar, M. (2018) Closed Form Exact Solutions to the Higher Dimensional Fractional Schrodinger Equation via the Modified Simple Equation Method. Journal of Applied Mathematics and Physics, 6, 90-102. doi: 10.4236/jamp.2018.61009.

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