Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations | Zendy

Chao Yue | Zendy; Guijuan Liu | Zendy; Kun Li | Zendy; Hanhui Dong | Zendy

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Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations

Author(s) -

Chao Yue,

Guijuan Liu,

Kun Li,

Hanhui Dong

Publication year - 2021

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2021/6670533

Subject(s) - matrix similarity , similarity (geometry) , mathematics , similarity solution , nonlinear system , mathematical analysis , scalar (mathematics) , fractional calculus , diffusion equation , diffusion , transformation (genetics) , partial differential equation , ordinary differential equation , differential equation , physics , geometry , thermodynamics , biochemistry , chemistry , economy , boundary layer , quantum mechanics , artificial intelligence , computer science , gene , economics , image (mathematics) , service (business)

By using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave similarity solution of time-fractional Harry Dym equation is presented. Furthermore, numerical solutions of time-fractional diffusion equation are discussed. Again, through another similarity transformation, nonlinear model of space-fractional diffusion/Harry Dym equation is turned into corresponding ordinary differential equations, whose two similarity solutions are also worked out.

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