Numerical solution for a variable-order fractional nonlinear cable equation via Chebyshev cardinal functions

DOI10.1134/S0965542517120120zbMath1393.65035OpenAlexW2789551588MaRDI QIDQ1746375

Somayeh Abdi-Mazraeh, Safar Irandoust-Pakchin, Ali Khani

Publication date: 25 April 2018

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542517120120

zbMATH Keywords

Caputo derivativeRiemann-Liouville derivativeoperational matrix of fractional derivativevariable-order fractional derivativenonlinear cable equation

Mathematics Subject Classification ID

Neural biology (92C20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Fractional derivatives and integrals (26A33) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)

Related Items (3)

Weak solvability of the variable-order subdiffusion equation ⋮ An efficient numerical algorithm for solving the two-dimensional fractional cable equation ⋮ A meshless method to solve the variable-order fractional diffusion problems with fourth-order derivative term

Cites Work

• Chebyshev cardinal functions: an effective tool for solving nonlinear Volterra and Fredholm integro-differential equations of fractional order
• On the selection and meaning of variable order operators for dynamic modeling
• Numerical solution of Riccati equation using the cubic B-spline scaling functions and Chebyshev cardinal functions
• Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term
• Numerical analysis for a variable-order nonlinear cable equation
• The use of Chebyshev cardinal functions for the solution of a partial differential equation with an unknown time-dependent coefficient subject to an extra measurement
• Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation
• Pseudodifferential operators with variable order of differentiation generating Feller semigroups
• On Markov process generated by pseudodifferential operator of variable order
• Variable order and distributed order fractional operators
• Feller semigroups obtained by variable order subordination
• Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation
• Numerical solution of fourth-order integro-differential equations using Chebyshev cardinal functions
• Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
• Mechanics with variable-order differential operators
• Embedding of function spaces of variable order of differentiation in function spaces of variable order of integration
• A variable order constitutive relation for viscoelasticity
• The use of Chebyshev cardinal functions for solution of the second‐order one‐dimensional telegraph equation

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