American Journal of Mathematical Analysis
ISSN (Print): 2333-8490 ISSN (Online): 2333-8431 Website: http://www.sciepub.com/journal/ajma Editor-in-chief: Grigori Rozenblum
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American Journal of Mathematical Analysis. 2015, 3(3), 72-84
DOI: 10.12691/ajma-3-3-3
Open AccessArticle

Solution of System of Linear Fractional Differential Equations with Modified Derivative of Jumarie Type

Uttam Ghosh1, 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, India

3Reactor Control Systems Design Section E & I Group B.A.R.C Mumbai India

4Department of Physics, Jadavpur University Kolkata;Department of Appl. Mathematics, University of Calcutta

Pub. Date: November 26, 2015

Cite this paper:
Uttam Ghosh, Susmita Sarkar and Shantanu Das. Solution of System of Linear Fractional Differential Equations with Modified Derivative of Jumarie Type. American Journal of Mathematical Analysis. 2015; 3(3):72-84. doi: 10.12691/ajma-3-3-3

Abstract

Solution of fractional differential equations is an emerging area of present day research because such equations arise in various applied fields. In this paper we have developed analytical method to solve the system of fractional differential equations in-terms of Mittag-Leffler function and generalized Sine and Cosine functions, where the fractional derivative operator is of Jumarie type. The use of Jumarie type fractional derivative, which is modified Rieman-Liouvellie fractional derivative, eases the solution to such fractional order systems. The use of this type of Jumarie fractional derivative gives a conjugation with classical methods of solution of system of linear integer order differential equations, by usage of Mittag-Leffler and generalized trigonometric functions. The ease of this method and its conjugation to classical method to solve system of linear fractional differential equation is appealing to researchers in fractional dynamic systems. Here after developing the method, the algorithm is applied in physical system of fractional differential equation. The analytical results obtained are then graphically plotted for several examples for system of linear fractional differential equation.

Keywords:
fractional calculus Jumarie fractional derivative Mittag-Leffler function generalized sine and cosine function fractional differential equations

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