American Journal of Mathematical Analysis
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American Journal of Mathematical Analysis. 2015, 3(2), 32-38
DOI: 10.12691/ajma-3-2-2
Open AccessArticle

Analytic Solution of Linear Fractional Differential Equation with Jumarie Derivative in Term of Mittag-Leffler Function

Uttam Ghosh1, , Srijan Sengupta2, Susmita Sarkar2 and Shantanu Das3, 4

1Department of Mathematics, Nabadwip Vidyasagar College, Nabadwip, Nadia, West Bengal, India

2Department of Applied Mathematics, University of Calcutta, Kolkata, West Bengal, India

3Reactor Control System Design Section Bhabha Atomic Research Centre, Mumbai, India

4Department of Physics, Jadavpur University Kolkata, West Bengal, India

Pub. Date: April 27, 2015

Cite this paper:
Uttam Ghosh, Srijan Sengupta, Susmita Sarkar and Shantanu Das. Analytic Solution of Linear Fractional Differential Equation with Jumarie Derivative in Term of Mittag-Leffler Function. American Journal of Mathematical Analysis. 2015; 3(2):32-38. doi: 10.12691/ajma-3-2-2

Abstract

There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied. Here we develop an algorithm to solve the linear fractional differential equation composed via Jumarie fractional derivative in terms of Mittag-Leffler function; and show its conjugation with ordinary calculus. In these fractional differential equations the one parameter Mittag-Leffler function plays the role similar as exponential function used in ordinary differential equations.

Keywords:
jumarrie fractional derivative riemann-liouvelli fractional derivative mittag-leffler function fractional differential equations

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