Solving inverse non-linear fractional differential equations by generalized Chelyshkov wavelets

Erman S., DEMİR A., Ozbilge E.

Alexandria Engineering Journal, vol.66, pp.947-956, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 66
  • Publication Date: 2023
  • Doi Number: 10.1016/j.aej.2022.10.063
  • Journal Name: Alexandria Engineering Journal
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, Directory of Open Access Journals
  • Page Numbers: pp.947-956
  • Keywords: Fractional differential equa-tion, Fractional order, Chelyshkov wavelet, Inverse problem, CHEBYSHEV COLLOCATION METHOD, REPRODUCING KERNEL-METHOD, NUMERICAL-SOLUTION, SYSTEMS
  • Kocaeli University Affiliated: Yes

Abstract

© 2022 THE AUTHORSThe purpose of this research is to employ a method involving Chelyshkov wavelets to construct a numerical solution to the inverse problem of determining the right-hand side function of a non-linear fractional differential equation by utilizing over-measured data. The novelty of this research is that this type of inverse problem is studied by Chelyshkov wavelets. Firstly, the problem is reduced into a system of algebraic equations with an unknown right-hand side by means of the orthonormal base of Chelyshkov wavelets. Secondly, by choosing suitable nodes, this system is transformed into a homogenous system of algebraic equations. The solution of the homogenous system allows us to determine the coefficients of the bases vectors for the solution of the non-linear fractional differential equation. In the final step, the right-hand side is obtained by substituting the constructed solution into a non-linear fractional differential equation. The presented examples illustrate that the numerical solution, obtained by this method, is remarkably close to the exact solution.