Analytical solutions for a time-fractional axisymmetric diffusion-wave equation with a source term

DOI10.1016/j.nonrwa.2010.11.015zbMath1216.35167OpenAlexW2033279524MaRDI QIDQ533076

Fangfang Zhang, Xiao-yun Jiang

Publication date: 2 May 2011

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2010.11.015

zbMATH Keywords

Mittag-Leffler functionintegral transformfractional diffusion-wave equationCaputo fractional derivative

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Mittag-Leffler functions and generalizations (33E12) Solutions to PDEs in closed form (35C05) Fractional partial differential equations (35R11)

Related Items

A modified fractional Landweber method for a backward problem for the inhomogeneous time-fractional diffusion equation in a cylinder ⋮ A compact finite difference scheme for the fourth-order fractional diffusion-wave system ⋮ Analytical solutions for multi-term time-space coupling fractional delay partial differential equations with mixed boundary conditions ⋮ Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative ⋮ Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions ⋮ Fractional differential equations and Lyapunov functionals ⋮ Analytical solutions for multi-term time-space fractional partial differential equations with nonlocal damping terms ⋮ Horizontal water flow in unsaturated porous media using a fractional integral method with an adaptive time step ⋮ Difference numerical solutions for time-space fractional advection diffusion equation ⋮ Analytical solutions for fractional partial delay differential-algebraic equations with Dirichlet boundary conditions defined on a finite domain

Cites Work

• Unnamed Item
• Unnamed Item
• Fractional diffusion-wave problem in cylindrical coordinates
• Fractional optimal control problem of a distributed system in cylindrical coordinates
• Decay of potential vortex for a viscoelastic fluid with fractional Maxwell model
• Signaling problem for time-fractional diffusion-wave equation in a half-space in the case of angular symmetry
• Some recent advances in theory and simulation of fractional diffusion processes
• The fractional diffusion model with an absorption term and modified Fick's law for non-local transport processes
• Fractals and fractional calculus in continuum mechanics
• Fox \(H\) functions in fractional diffusion
• Finite difference approximations for fractional advection-dispersion flow equations
• Decay of a potential vortex in a generalized Oldroyd-B fluid
• Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation
• Some exact solutions for the helical flow of a generalized Oldroyd-B fluid in a circular cylinder
• Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term
• Fundamental solutions to three-dimensional diffusion-wave equation and associated diffusive stresses

This page was built for publication: Analytical solutions for a time-fractional axisymmetric diffusion-wave equation with a source term