A method for obtaining the operational matrix of fractional Jacobi functions and applications

作者：Kayedi Bardeh Amin; Eslahchi M R^*; Dehghan Mehdi

来源：Journal of Vibration and Control, 2014, 20(5): 736-748.

DOI：10.1177/1077546312467049

• Operational matrix
• Caputo derivative
• fractional Jacobi functions
• Taylor series
• analytical functions
• orthogonal expansion
• spectral collocation method
• fractional differential equations
• fractional integro-differential equations

In this paper we first introduce fractional orthogonal Jacobi functions then we obtain a new fractional derivative operational matrix for these orthogonal functions. It is based on the relationship between the coefficients of the fractional Taylor series and fractional Jacobi function expansions. We also apply this new operational matrix to the collocation method for solving general multi-order fractional differential equations (FDEs) and nonlinear fractional integro-differential equations (FIDEs). We also present several test problems. The numerical results show that our new scheme is very effective and convenient for solving FDEs and FIDEs.

• 出版日期2014-4