[PDF] Top 20 Second order numerical methods for the tempered fractional diffusion equations

... many fractional models [1–18, 21, 22, 24–27] with (tempered) fractional derivatives have been widely applied in many fields of science and technology, a lot of re- search results have been ...of ... See full document

... Fractional order differential equations are used in modeling of many phenomena in engineering, chemistry, physics, finance, and other disciplines, see [8, 14, 19] and the references ...most ... See full document

... time fractional derivative. In [10], Hristov proposes new equations related to the fractional diffusion equations using the Atangana-Baleanu fractional derivative, see others ... See full document

... The numerical experiment results revealed that this method is more accurate and efficient in comparison with some compact finite difference ...the fractional-order Legendre func- tions for solving the ... See full document

... The numerical methods for fractional differential equations [6] have been heated discussion in domestic and foreign recently, including time and space fractional derivative, single and ... See full document

... advection-diffusion-reaction equations, that may include stiff reactive terms, as hyperbolic balance laws with stiff source ...the order of accuracy r of the numerical scheme used, the mesh ... See full document

... several numerical and analytical methods of solution have been adopted to solve both linear and nonlinear equations [38, ...tau methods [4, 26, 32, 34, 36, 39, 40] to mention a ...of ... See full document

... Riesz fractional derivative. At first, the Riesz fractional derivative was generally approached by the Grünwald-Letnikov derivative ap- proximation with the first order of accuracy ...In order ... See full document

... involving fractional calculus is already very large and still ...the fractional calculus is that the fractional derivatives provide an excellent approach for the description of memory and hereditary ... See full document

... Riesz tempered fractional diffusion equation with a nonlinear source term, where the tempered fractional partial derivatives are evaluated by the modified second-order Lubich ... See full document

... the tempered-FDEs, and the desired order in space and time is ...convergent. Numerical examples are presented in Section  to verify our theoretical ... See full document

... For numerical ap- proximations of 1D fractional diffusion equation Bahsi and Yalcinbas [10] cho- sen Fibonacci polynomials to express the trial solution in both space and time domain and then used ... See full document

... inversion numerical method to approximate the fractional order differential ...proposed numerical method mainly depends on the optimal selection of contour of ...approximate fractional ... See full document

... Can we follow the same approach for the other differential equations? Well, usually no, we can’t. The reason this worked so nicely in o ur first example was that the two sides of the equation were neatly separated ... See full document

... a numerical method for solving a class of fractional convection diffusion equations with time-space variable ...considered equations will be reduced to the corresponding systems of ... See full document

... the diffusion and the time scale of the effective force field since the latter depends on the concentration of another diffusing ...the fractional Nernst-Planck equation considered in [35, 36] the force ... See full document

... hybrid methods for solving second order ordinary differential ...From numerical observations, we conclude that the phase fitted and amplification fitted explicit hybrid methods are very ... See full document

... [21] P. Onumanyi, D. O. Awoyemi, S. N. Jator, and U. W. Sirisena, New linear mutlistep methods with continuous coefficients for first order initial value problems, J. Niger. Math. Soc. 13, (1994), 37 51. ... See full document

... these equations, many other interesting methods for the approximated solution and stability procedure are available in earlier literature [1, 2, 3, 4, 5, 6, 9, 10, 12, ... See full document

... Riemann-Liouville fractional derivative appears unsuitable to be treated by the Laplace transform technique in that it requires the knowledge of the non-integer order derivatives of the function at t = 0 ... See full document