TY - JOUR ID - 868 TI - Numerical approach for solving a class of nonlinear fractional differential equation JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Irandoust-pakchin, S. AU - Lakestani, M. AU - ‎Kheiri, H. AD - Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences, University of Tabriz‎, ‎Tabriz‎, ‎Iran. Y1 - 2016 PY - 2016 VL - 42 IS - 5 SP - 1107 EP - 1126 KW - Fractional-order differential equation‎ KW - ‎operational matrix‎ ‎of fractional derivative‎ KW - ‎Caputo derivative‎ KW - ‎Chebyshev cardinal function‎ KW - ‎collocation method‎ DO - N2 - ‎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. UR - http://bims.iranjournals.ir/article_868.html L1 - http://bims.iranjournals.ir/article_868_26827a7d21fe2b110ccd0dc9c647f92a.pdf ER -