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- W4311004145 abstract "Abstract This research presents a numerical approach to obtain the approximate solution of the n-dimensional co-homological equations of fractional order in continuous-time dynamical systems. For this purpose, the n-dimensional fractional Müntz-Legendre polynomials (or n-DFMLPs) are introduced. The operational matrix of the fractional Riemann-Liouville derivative is constructed by employing n-DFMLPs. Our method transforms the cohomological equation of fractional order into a system of algebraic equations. Therefore, the solution of that system of algebraic equations is the solution of the associated cohomological equation. The existence of solution for FCEs by means of classical fixed point theory is proven. Also, the stability of the approximate solution of the cohomological equation is checked with respect to a small perturbation of the function g(x) . The error bound and convergence analysis of the applied method under the L 2 -norm is discussed. Some examples are considered and discussed to confirm the efficiency and accuracy of our method. The actual error is computed and compared for different values of k as the number of n-DFMLPs. Mathematics Subject Classification (2020) : 37C05, 35R11" @default.
- W4311004145 created "2022-12-22" @default.
- W4311004145 creator A5025794259 @default.
- W4311004145 creator A5031081893 @default.
- W4311004145 date "2022-11-30" @default.
- W4311004145 modified "2023-09-26" @default.
- W4311004145 title "A numerical approach based on n-dimensional fractional Müntz-Legendre polynomials for solving fractional-order cohomological equations with variable coefficients" @default.
- W4311004145 doi "https://doi.org/10.21203/rs.3.rs-2312082/v1" @default.
- W4311004145 hasPublicationYear "2022" @default.
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