A novel direct method based on the Lucas multiwavelet functions for variable‐order fractional reaction‐diffusion and subdiffusion equations

Abstract

In this article, we study the numerical technique for variable‐order fractional reaction‐diffusion and subdiffusion equations that the fractional derivative is described in Caputo's sense. The discrete scheme is developed based on Lucas multiwavelet functions and also modified and pseudo‐operational matrices. Under suitable properties of these matrices, we present the computational algorithm with high accuracy for solving the proposed problems. Modified and pseudo‐operational matrices are employed to achieve the nonlinear algebraic equation corresponding to the proposed problems. In addition, the convergence of the approximate solution to the exact solution is proven by providing an upper bound of error estimate. Numerical experiments for both classes of problems are presented to confirm our theoretical analysis.

Speech scrambling based on multiwavelet and Arnold transformations

“…The standard procedure entails processing each of the rows in sequential order, followed by handling each column of the output in turn. Methods that cannot be separated into two distinct categories function in both dimensions of speech simultaneously [25]. Scalars are used in the computation of discrete multiwavelet transform.…”

Regularity theory for fractional reaction–subdiffusion equation and application to inverse problem

“…This equation was introduced and analyzed in Seki et al 14 and Yuste et al 15 in order to establish the reaction-subdiffusion processes of both the motion and reaction terms which move and interact with each other under the influence of the subdiffusive nature of the processes. For more details on the formulation of FrRSE and its chemical meaning, one can consult Seki et al 14 and Yuste et al 15 After the works of Seki et al 14 and of Yuste et al 15 above, there are various numerical schemes that have been proposed to find the approximation solutions for both linear and nonlinear FrRSEs; see, for example, previous studies [16][17][18][19][20][21][22][23] among others and the references given therein.…”

Vieta–Fibonacci wavelets: Application in solving fractional pantograph equations

“…In Rahimkhani and Ordokhani, 18 the authors used the Bernoulli wavelets for solving some astrophysics problems. The authors of Dehestani et al 19 applied the Lucas wavelets for solving fractional sub-diffusion and reaction-diffusion equations. The Fibonacci wavelets in Sabermahani and Ordokhani 20 and the Boubaker wavelets in Rabiei and Ordokhani 21 have been used to solve optimal control problems.…”