Quantum mechanics

Service (business)

Materials science

Boundary value problem

Applied mathematics

Convergence (economics)

Wave equation

Variable (mathematics)

Economics

Computer science

Dirichlet boundary condition

Matrix (chemical analysis)

Thermodynamics

Algebraic equation

Physics

Nonlinear system

Collocation (remote sensing)

Diffusion

Mathematics

Mathematical analysis

Artificial intelligence

Composite material

Economy

Economic growth

Diffusion equation

Finance

Term (time)

Fractional calculus

Order (exchange)

Machine learning

Wavelet

Applied Mathematics and Computation

We firstly generalize a multi-term time fractional diffusion-wave equation to the multi-term variable-order time fractional diffusion-wave equation (M-V-TFD-E) by the concept of variable-order fractional derivatives. Then we implement the Chebyshev wavelets (CWs) through the operational matrix method to approximate its solution in the unit square. In fact, we apply the operational matrix of variable-order fractional derivative (OMV-FD) of the CWs to derive the unknown solution. We proceed with coupling the collocation and tau methods to reduce M-V-TFD-E to a system of algebraic equations. The important privilege of method is handling different kinds of conditions, i.e., initial-boundary conditions and Dirichlet boundary conditions, by implementing the same techniques. The convergence and error estimation of the CWs expansion in two dimensions are theoretically investigated. We also examine the applicability and computational efficiency of the new scheme through the numerical experiments.

A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation