hadi rezazadeh - Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, P.O. Box ۱۹۱۴, Rasht, Iran
hossein aminikhah - Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, P.O. Box ۱۹۱۴, Rasht, Iran,

In this paper, we develop a new application of Laplace's transform of fractional order for solving linear fractional differential equations. The fractional derivatives are described by modified Riemann-Liouville derivative. To illustrate the reliability of the method, some examples are provided. The obtained solutions show that the present method is an efficient and simple tool for solving linear fractional differential equations within the modified Riemann-Liouville derivative.

Mittag-Leffler function, Laplace's transform, Fractional derivative, Modified Riemann-Liouville