A hybrid approach established upon the Müntz‐Legender functions and 2D Müntz‐Legender wavelets for fractional Sobolev equation

Abstract

This article proposes a hybrid technique for finding approximation solutions of the fractional 2D Sobolev equation. In the proposed approach, the Müntz-Legender functions and Müntz-Legender wavelets are, respectively, utilized to approximate the solution of the problem under consideration in the time and spatial directions. By implementing the presented technique, solving the 2D fractional Sobolev equation is converted into solving a system of algebraic equations. Three examples are solved to examine the validity of the proposed method.

Dynamic vibration analysis of cantilever beams on nonlinear fractional viscoelastic foundation under Gaussian white noise

“…Tural-Polat et al 28 used third class shifted Chebyshev polynomials (SCP3) to approximate multinomial VO FDEs to achieve an efficient numerical solution. Hosseininia et al 29 successfully solved the time fractional three-dimensional Sobolev equations using two-dimensional shifted Chebyshev basis polynomials of the second class and twodimensional shifted Chebyshev polynomials of the second class. To solve this problem, we use a shifted Chebyshev polynomial algorithm, which can solve nonlinear fractional order equations efficiently and directly in the time domain.…”

A hybrid spectral approach based on 2D cardinal and classical second kind Chebyshev polynomials for time fractional 3D Sobolev equation

“…Moreover, it explains the moisture migration in soil [22] and thermodynamics [23]. In recent years, many numerical methods, such as the local discontinuous Galerkin method [24], local meshless radial basis function method [25], Bernoulli polynomials spectral method [26], and a hybrid technique of the Müntz–Legendre functions and 2D Müntz–Legendre wavelets [27], have been adopted to solve different fractional versions of the Sobolev equation.…”