time-fractional diffusion wave equation
Solutions to Time Fractional Diffusion Wave Equation in Cylindrical Coordinates
... to time-fractional diffusion-wave equation with a source term in cylindrical coordinates are obtained for an infinite ...to time t, the Hankel transform with respect to the radial ...
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On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation
... particular cases of the fundamental solution G α,β,n in terms of the Wright type functions. Discussion 325[r] ...
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A numerical algorithm based on modified extended B spline functions for solving time fractional diffusion wave equation involving reaction and damping terms
... a time-fractional DWE involving reaction and damping ...Caputo’s time-fractional derivative has been used, while spatial derivatives are described by modi- fied ECBS ...
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A finite difference scheme based on cubic trigonometric B splines for a time fractional diffusion wave equation
... The outline of this paper is as follows. In Section , we give temporal discretization using a forward finite difference scheme of Eq. (). In Section , we present the derivation of the scheme for the fractional ...
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Numerical solution of fractional diffusion wave equation and fractional Klein–Gordon equation via two dimensional Genocchi polynomials with a Ritz–Galerkin method
... the time-fractional diffusion-wave equation was developed by ...the time-fractional diffusion wave equation in ...
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From Newton's Equation to Fractional Diffusion and Wave Equations
... for fractional calculus would be the modellization of the shape memory alloys ...in time through integrodifferential equations and, possibly, fractional differential ...
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Abstract Fractional sine transform and Laplace transform are used for solving the Stokes` first problem with
... of fractional of fractional partial differential equations of the time fractional advection dispersion equation as in[6,7], fractional diffusion equation as ...
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Approximate Solution For Time-Space Fractional Soil Moisture Diffusion Equation And Its Application
... scenario fractional calculus plays an important role in the various fields of scientific and engineering ...problems. Fractional calculus is a field of mathematical study that grows out of the traditional ...
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Analysis of two Legendre spectral approximations for the variable coefficient fractional diffusion wave equation
... variable-coefficient fractional diffusion-wave equation in a bounded domain by the Legendre spectral ...The time fractional derivative is in the Caputo sense of order γ ∈ (1, ...the ...
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Difference numerical solutions for time-space fractional advection diffusion equation
... A time-space fractional advection diffusion equation is studied in this paper. Based on the difference method, an explicit difference scheme and an implicit difference scheme are obtained. Then we prove ...
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Existence results for a generalization of the time-fractional diffusion equation with variable coefficients
... a contractible mapping to show the existence of solution of the semilinear problem in a suitable fractional derivative Sobolev space. The main idea is motivated in the proof of [32, 33]. The existence of solutions ...
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Solution of a modified fractional diffusion equation
... where 0 < α < β ≤ 1 and A and B are positive dimensionless constants. A possible application of this equation is in econophysics where there is an in- creasing interest in modelling using CTRWs [28–34]. In ...
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Anomalous nonlinear dielectric and Kerr effect relaxation steady state responses in superimposed ac and dc electric fields
... fixed time, so that the only random variable is the direction of the ...Cole-Cole equation 共1兲 is concerned, we first remark that ...the diffusion limit of a continuous time random walk ...
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Fractional diffusion: biological models and nonlinear problems driven by the s-power of the Laplacian.
... of diffusion-type equations from the transport equations through the asymptotic analysis it is possible using a particular scaling corresponding to a long ...a diffusion type equation starting from a ...
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The Wave Equation and General Plane Wave Solutions in Fractional Space
... of fractional space in electromagnetic research include the derivation of Gauss law in D-dimensional fractional space [3], solution of electrostatic problem in D-dimensional fractional space (2 < ...
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The dependence of blow-up time with respect to parameters for small reaction diffusion equation
... finite time when is small enough in addition, we prove that the semi discrete blow- up time tends to the real one as $\gamma$ goes to ...blow-up time converges to the real one when the mesh size ...
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The Traveling Wave Solutions of Space Time Fractional Differential Equation Using Fractional Riccati Expansion Method
... the fractional transformation U ( ) ξ contains only one term, formula (5) is ...new fractional Riccati expansion ...transform fractional partial differential equations into fractional ordinary ...
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Solving nonlinear space-time fractional differential equations via ansatz method
... There are several approaches to the generalization of the notion of differentiation to fractional orders e.g. Gr¨ unwald–Letnikow, Caputo and Riemann–Liouville [20, 58]. Modified Riemann-Liouville derivative is ...
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Landweber iterative regularization method for identifying the unknown source of the time fractional diffusion equation
... In this paper, we investigate an inverse problem to determine an unknown source term that has a separable-variable form in the time-fractional diffusion equation, whereby the data is obtained at a ...
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New Modified Method of the Chebyshev Collocation Method for Solving Fractional Diffusion Equation
... Fokker-Planck equation into a system of ordinary differential equations suggested in( [15], [16]) ...space fractional diffusion equations are solved numerically ...space fractional ...
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