Numerical approach for solving a class of nonlinear fractional differential equation

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.