Available online at www.isr-publications.com/jmcs J. Math. Computer Sci. 16 (2016), 147–153 Research Article Variation of parameters for local fractional nonhomogenous linear-differential equations Mohammed AL Horani a,b , Mamon Abu Hammad b , Roshdi Khalil b,* a Department of Mathematics, Faculty of Science, University of Hail, Saudi Arabia. b Department of Mathematics, The University of Jordan, Amman, Jordan. Abstract In this paper we study the method of variation of parameters to find a particular solution of a nonhomogenous linear fractional differential equations. A formula similar to that for usual ordinary differential equations is obtained. c 2016 All rights reserved. Keywords: Conformable fractional derivative, fractional integral, fractional differential equation, variation of parameters. 2010 MSC: 26A33. 1. Introduction There are many definitions available in the literature for fractional derivatives. The main ones are the Riemann Liouville definition and the Caputo definition, see [10, 11], and for some applications one can see [5], [8] and [12]. (i) Riemann - Liouville Definition. For α ∈ [n − 1,n), the α derivative of f is D α a (f )(t)= 1 Γ(n − α) d n dt n t  a f (x) (t − x) α-n+1 dx. * Corresponding author Email addresses: m.alhorani@uoh.edu.sa (Mohammed AL Horani), roshdi@ju.edu.jo (Roshdi Khalil) Received 2016-01-09