Quantum mechanics

Discretization

Applied mathematics

Regularized meshless method

Computer science

Thermodynamics

Physics

Finite element method

Singular boundary method

Mathematics

Mathematical analysis

Geometry

Boundary element method

Numerical analysis

Time derivative

Symmetry (geometry)

Partial differential equation

Term (time)

Artificial neural network

Fractional calculus

Machine learning

Radial basis function

Symmetry

Fractional differential equations depict nature sufficiently in light of the symmetry properties which describe biological and physical processes. This article is concerned with the numerical treatment of three-term time fractional-order multi-dimensional diffusion equations by using an efficient local meshless method. The space derivative of the models is discretized by the proposed meshless procedure based on the multiquadric radial basis function though the time-fractional part is discretized by Liouville–Caputo fractional derivative. The numerical results are obtained for one-, two- and three-dimensional cases on rectangular and non-rectangular computational domains which verify the validity, efficiency and accuracy of the method.

Solution of Multi-Term Time-Fractional PDE Models Arising in Mathematical Biology and Physics by Local Meshless Method