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), 54-64
DOI: 10.12691/ajma-3-3-1
Open AccessArticle

Solutions of Linear Fractional non-Homogeneous Differential Equations with Jumarie Fractional Derivative and Evaluation of Particular Integrals

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 System Design Section Bhabha Atomic Research Centre, Mumbai, India

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

Pub. Date: September 10, 2015

Cite this paper:
Uttam Ghosh, Susmita Sarkar and Shantanu Das. Solutions of Linear Fractional non-Homogeneous Differential Equations with Jumarie Fractional Derivative and Evaluation of Particular Integrals. American Journal of Mathematical Analysis. 2015; 3(3):54-64. doi: 10.12691/ajma-3-3-1

Abstract

In this paper we describe a method to solve the linear non-homogeneous fractional differential equations (FDE), composed with Jumarie type fractional derivative, and describe this method developed by us, to find out particular integrals, for several types of forcing functions. The solutions are obtained in terms of Mittag-Leffler functions, fractional sine and cosine functions. We have used our earlier developed method of finding solution to homogeneous FDE composed via Jumarie fractional derivative, and extended this to non-homogeneous FDE. We have demonstrated these developed methods with few examples of FDE, and also applied in fractional damped forced differential equation. The short cut rules, that are developed here in this paper to replace the operator Da or operator D2a as were used in classical calculus, gives ease in evaluating particular integrals. Therefore this method proposed by us is useful and advantageous as it is having conjugation with the classical methods of solving non-homogeneous linear differential equations, and also useful in understanding physical systems described by FDE.

Keywords:
Mittag-Leffler functions non-homogeneous fractional differential equations modified riemann-liouville definition

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