TY - JOUR
ID - 5902
TI - The operational matrix of fractional derivative of the fractional-order Chebyshev functions and its applications
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Ahmadi Darani, Mohammadreza
AU - Saadatmandi, Abbas
AD - Department of Applied Mathematics, Faculty of Mathematical Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran
AD - Department of Applied Mathematics, Faculty of Mathematical Sciences,
University of Kashan, Kashan, 87317-51167, Iran
Y1 - 2017
PY - 2017
VL - 5
IS - 1
SP - 67
EP - 87
KW - Chebyshev polynomials
KW - orthogonal system
KW - fractional differential equation
KW - fractional-order Chebyshev functions
KW - Operational matrix
DO -
N2 - In this paper, we introduce a family of fractional-order Chebyshev functions basedÂ on the classical Chebyshev polynomials. We calculate and derive the operational matrix of derivative of fractional order $gamma$ in the Caputo sense using the fractional-order Chebyshev functions. This matrix yields to low computational cost of numerical solution of fractional order differential equations to the solution of a system of algebraic equations. Several numerical examples are given to illustrate the accuracy of our method. The results obtained, are in full agreement with the analytical solutions and numerical results presented by some previous works.
UR - https://cmde.tabrizu.ac.ir/article_5902.html
L1 - https://cmde.tabrizu.ac.ir/article_5902_97563e2dfae2abcda93be4bd14ba9e1c.pdf
ER -