Numerical solutions for the reaction–diffusion, diffusion‐wave, and Cattaneo equations using a new operational matrix for the Caputo–Fabrizio derivative
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6517
Abstract: In this research work, we study the model of nonlinear reaction–diffusion equation, diffusion‐wave equation, and Cattaneo equation with the help of a numerical method in which time‐fractional derivative is of Caputo–Fabrizio type (C‐F). First, we… read more here.
Keywords: operational matrix; diffusion; equation; diffusion wave ... See more keywords
An efficient meshless method based on RBFs for the time fractional diffusion-wave equation
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DOI: 10.1007/s13370-018-0616-y
Abstract: This paper proposes a numerical method to deal with time-fractional diffusion-wave equation (one-dimensional and two-dimensional). The time-fractional term of the problem is scheduled in Caputo sense which is popular in analyzing time-fractional dependent problems. The… read more here.
Keywords: fractional diffusion; time fractional; time; method ... See more keywords
Analysis of the Time Fractional 2-D Diffusion-Wave Equation via Moving Least Square (MLS) Approximation
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DOI: 10.1007/s40819-016-0247-7
Abstract: In this paper, the time fractional two-dimensional diffusion-wave equation defined by Caputo sense for ($$1 read more here.
Keywords: approximation; moving least; time fractional; diffusion wave ... See more keywords
The pointwise estimates of diffusion wave of the compressible micropolar fluids
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DOI: 10.1016/j.jde.2018.04.039
Abstract: Abstract The pointwise estimates for the compressible micropolar fluids in dimension three are given, which exhibit generalized Huygens' principle for the fluid density and fluid momentum as the compressible Navier–Stokes equation, while the micro-rational momentum… read more here.
Keywords: micropolar fluids; pointwise estimates; compressible micropolar; diffusion wave ... See more keywords
Analysis of a robust implicit scheme for space–time fractional stochastic nonlinear diffusion wave model
Sign Up to like & getrecommendations! Published in 2023 at "International Journal of Computer Mathematics"
DOI: 10.1080/00207160.2023.2207677
Abstract: The current paper develops and analyzes a numerical scheme for the space–time fractional stochastic nonlinear diffusion wave equations. The implicit scheme is based on the matrix transform technique for discretizing the Riesz-space fractional derivative, -order… read more here.
Keywords: time; diffusion wave; space; scheme ... See more keywords
Transient response of a hygrothermoelastic cylinder based on fractional diffusion wave theory
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Thermal Stresses"
DOI: 10.1080/01495739.2017.1344111
Abstract: ABSTRACT A coupled fractional hygrothermoelasticity theory is formulated within the framework of fractional calculus. Both the classical Fourier’s and Fick’s laws are generalized to anomalous diffusion which is characterized by the time- fractional diffusion-wave equation.… read more here.
Keywords: fractional diffusion; diffusion; transient response; diffusion wave ... See more keywords
Subordination in a class of generalized time-fractional diffusion-wave equations
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DOI: 10.1515/fca-2018-0048
Abstract: Abstract Motivated by recently proposed generalizations of the diffusion-wave equation with the Caputo time fractional derivative of order α ∈ (1, 2), in the present survey paper a class of generalized time-fractional diffusion-wave equations is… read more here.
Keywords: class; time fractional; diffusion wave; fractional diffusion ... See more keywords
The Truncation Regularization Method for Identifying the Initial Value on Non-Homogeneous Time-Fractional Diffusion-Wave Equations
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DOI: 10.3390/math7111007
Abstract: In the essay, we consider an initial value question for a mixed initial-boundary value of time-fractional diffusion-wave equations. This matter is an ill-posed problem; the solution relies discontinuously on the measured information. The truncation regularization… read more here.
Keywords: fractional diffusion; time fractional; initial value; value ... See more keywords
Theoretical Analysis (Convergence and Stability) of a Difference Approximation for Multiterm Time Fractional Convection Diffusion-Wave Equations with Delay
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DOI: 10.3390/math8101696
Abstract: In this paper, we introduce a high order numerical approximation method for convection diffusion wave equations armed with a multiterm time fractional Caputo operator and a nonlinear fixed time delay. A temporal second-order scheme which… read more here.
Keywords: time; diffusion wave; convection diffusion; multiterm time ... See more keywords
A Study on Fractional Diffusion - Wave Equation with a Reaction
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DOI: 10.3390/sym14081537
Abstract: An analytical method for solving the fractional diffusion–wave equation with a reaction is investigated. This approach is based on the Laplace transform and fractional series method. An analytical derivation for the proposed method is presented.… read more here.
Keywords: fractional diffusion; diffusion wave; wave equation; method ... See more keywords