RATIONAL APPROXIMATIONS FOR SOLVING DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER ON SEMI-INFINITE INTERVAL

摘要

In this paper, a generalization of rational Chebyshev functions and named fractional rational Chebyshev functions, is introduced for solving fractional differential equations. By using the collocation scheme, the efficiency and performance of the new basis is shown through several examples. Also, the obtained results are compared with rational Chebyshev results. "It is shown that the generalized functions are more efficient to solve fractional differential equations, and they converge more rapidly.