Numerical solution fractional-order Chebyshev wavelets combining SA algorithm for solving fractional differential equations
An effective numerical method is developed based on the collocation method of fractional-order Chebyshev wavelets(FOCWs)of the second kind,combining simulated annealing(SA)algorithm for the numerical solution of fractional differential equations.First,the fractional-order Chebyshev wavelets of the second kind were constructed.Then,using the regularized Beta function,the exact formulas of FOCWs were derived under the definition of Riemann-Liouville fractional integral.By the properties of FOCWs and the exact formulas together with the collocation method,the problem under consideration was simplified into algebraic equations.The error analysis of the proposed method is studied.Due to the involvement of parameter α in FOCWs method,the accuracy of the solution depends on the selection of parameter α.SA algorithm was considered to find the optimal parameter α.Finally,the effectiveness and applicability of the suggested method are verified by some numerical examples.