Results 21 to 30 of about 3,658,729 (281)
On a new class of fractional partial differential equations II [PDF]
Advances in Calculus of Variations, 2014 Abstract In this paper we continue to advance the theory regarding the Riesz fractional gradient in the calculus of variations and fractional partial differential equations begun in an earlier work of the same name. In particular, we here establish an
Shieh, Tien-Tsan, Spector, Daniel E.
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Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations
Complexity, 2020 In this paper, three types of fractional order partial differential equations, including the fractional Cauchy–Riemann equation, fractional acoustic wave equation, and two-dimensional space partial differential equation with time-fractional-order, are ...
Haidong Qu, Zihang She, Xuan Liu
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Multigrid methods for space fractional partial differential equations [PDF]
Journal of Computational Physics, 2015 We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means the convergence rates of the methods are independent of the mesh size and mesh level.
Ying-Jun Jiang, Xuejun Xu
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Ain Shams Engineering Journal, 2014 In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear ...
Ahmet Bekir, Özkan Güner
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A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations
The Scientific World Journal, 2014 We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations.
Özkan Güner, Adem C. Cevikel
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Journal of Taibah University for Science, 2022 In this study, the extended tanh-function method has been used to find further general travelling wave solutions for space-time fractional nonlinear partial differential equations, namely, the time fractional nonlinear Sine-Gordon equation and Klein ...
Umme Sadiya +3 more
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Converting fractional differential equations into partial differential equations
Thermal Science, 2012 A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.
Ji-Huan He, Zheng-Biao Li
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Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations
Mathematics, 2016 Fourier spectral methods for solving some linear stochastic space-fractional partial differential equations perturbed by space-time white noises in the one-dimensional case are introduced and analysed.
Yanmei Liu, Monzorul Khan, Yubin Yan
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Numerical Solution of Parabolic Equations by the Box Scheme [PDF]
, 1973 The box scheme proposed by H. B. Keller is a numerical method for solving parabolic partial differential equations. We give a convergence proof of this scheme for the heat equation, for a linear parabolic system, and for a class of nonlinear parabolic ...
Fong, Kirby William
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SOLVABILITY OF HYPERBOLIC FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS
Journal of Applied Analysis & Computation, 2017 Summary: The main purpose of this paper is to study the existence and uniqueness of solutions for the hyperbolic fractional differential equations with integral conditions. Under suitable assumptions, the results are established by using an energy integral method which is based on constructing an appropriate multiplier.
Akilandeeswari, Aruchamy +2 more
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