An Application of Müntz Wavelets Galerkin Method for Solving the Fractional Differential Equations

Çınar M., Seçer A.

IInternational Conference on Mathematical Advances and Applications, İstanbul, Turkey, 24 - 27 June 2020, pp.3-4, (Summary Text)

  • Publication Type: Conference Paper / Summary Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.3-4
  • Yıldız Technical University Affiliated: Yes

Abstract

In this study, the Müntz wavelet which is a one of the quitely fresh wavelet types is considered to derive a solution of the fractional differential equations in Caputo sense. The Müntz wavelets can be differently expressed using Müntz-Legendre polynomials [1], Jacobi polynomials [2] or modified Müntz formula [3]. The operational matrices for fractional integration and derivative operators are given for Müntz wavelets [4]. The basis of wavelets is a powerful tool for solving integral and differential equations. The main difference between Haar, Legendre, Chebyshev wavelets and Müntz wavelets is in their degree of the extended sentences. Since the degrees of the Müntz polynomials are complex, Müntz wavelets both present a high accuracy for all complex functions or functions with fractional powers and also cover a broad range of functions primarily occuring in fractional models. The one of the advantages of the method is that the used method enables a simple procedure to convert the differential or integral equations to an algebraic system to be simply solved by many conventional methods in the literature. The procedure for solving equation is tested on some examples to show the applicability, efficiency and accuracy of the used method. The numerical computations in this study are done by using Maple software. The values obtained from the solution of the considered equation by Müntz wavelet method are compared with the other numeric and exact solution in the literature. The comparison of approximate and analytic solution of the problem are visualized by graphics and the errors between the solutions are comparatively shown in the tables. The numerical findings show that the method is quitely effective since it has easy algorithm, high accuracy, less computational complexity and less CPU time for solving the considered equation.

Keywords: Fractional differential equations, Müntz wavelet, numeric methods