Document Type : Research Paper

**Authors**

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.

**Abstract**

It is commonly accepted that fractional differential equations play an important role in the explanation of many physical phenomena. For this reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solution of a class of fractional differential equation. The fractional derivatives are described based on the Caputo sense. Our main aim is to generalize the Chebyshev cardinal operational matrix to the fractional calculus. In this work, the Chebyshev cardinal functions together with the Chebyshev cardinal operational matrix of fractional derivatives are used for numerical solution of a class of fractional differential equations. The main advantage of this approach is that it reduces fractional problems to a system of algebraic equations. The method is applied to solve nonlinear fractional differential equations. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

**Keywords**

- Fractional-order differential equation
- operational matrix of fractional derivative
- Caputo derivative
- Chebyshev cardinal function
- collocation method

**Main Subjects**

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October 2016

Pages 1107-1126

**Receive Date:**10 January 2015**Revise Date:**05 July 2015**Accept Date:**05 July 2015