Solution for a Fractional Diffusion-Wave Equation Defined in a Bounded Domain

By Om Prakash Agrawal. 2002

505 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/17b940b6e297650e8f7f3a1f9612209a56947e61

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In Mechanics of Materials

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Distributed-order fractional diffusions on bounded domains (2009, methodology): “Agrawal [1] worked with single-order fractional Cauchy problem with Dirichlet boundary conditions.”
Variational iteration method for fractional heat- and wave-like equations (2009, background): “(1) reduce to the fractional wave-like equation which models anomalous diffusive and subdiffusive systems, description of fractional random walk, unification of diffusion and wave propagation phenomena [40] [41] [42] [43].”
Analytical solution for the time-fractional telegraph equation by the method of separating variables (2008, background): “[24] O.P. Agrawal, Solution for a fractional diffusion–wave equation defined in a bounded domain, J. Nonlinear Dynam.”
Finite difference/spectral approximations for the time-fractional diffusion equation (2007, unknown): “3) can be obtained [1] as uðx; tÞ 1⁄4 2 L X1 n1⁄40 Eað a(2)n(2)tÞ sinðanxÞ Z L”
Boundary value problems for multi-term fractional differential equations (2008, methodology): “Agrawal [11] has solved fractional diffusion equation using finite sine transform method, and Metzler and Klafter [6] have employed the method of images and Fourier–Laplace transform.”
Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems (2011, methodology): “Agarwal [3] solved a fractional diffusion equation using a finite sine transform technique and presented numerical results in a one-dimensional bounded domain.”
Analytical solutions for the multi-term time–space Caputo–Riesz fractional advection–diffusion equations on a finite domain (2012, background): “The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2] and [0,2], respectively.”
Existence and Uniqueness results for a class of Generalized Fractional Differential Equations (2014, background): “Agrawal discusses diffusion and heat equations of fractional order in [2–4].”
Solving a fourth‐order fractional diffusion‐wave equation in a bounded domain by decomposition method (2008, methodology): “The time fractional diffusion-wave equation [1] is obtained from the classical diffusion or wave equation by replacing the first-or second order time derivative by a fractional derivative of order α with 0 < α < 1 or 1 < α < 2, respectively [2].”