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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Converting Fractional Differential Equations Into Partial Differential Equations, Ji-Huan He, Zheng-Biao Li
Converting Fractional Differential Equations Into Partial Differential Equations, Ji-Huan He, Zheng-Biao Li
Ji-Huan He
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.
Asymptotic Methods For Solitary Solutions And Compactons, Ji-Huan He
Asymptotic Methods For Solitary Solutions And Compactons, Ji-Huan He
Ji-Huan He
This review is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations . Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace Transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this review article are first appeared. …
A Remark On "A Nonlinear Mathematical Model Of The Corneal Shape", Ji-Huan He
A Remark On "A Nonlinear Mathematical Model Of The Corneal Shape", Ji-Huan He
Ji-Huan He
An analytical method using Taylor series is proposed to solve a nonlinear two-point boundary problem arising in corneal shape. The solution process makes it extremely easy to obtain a relatively accurate solution. The pencil-and-paper solution procedure can be extended to other boundary value problems.