Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions

Latterly, many problems arising in different fields of science and engineering can be reduced, by applying some appropriate discretization, to a series of time-fractional partial differential equations. Unlike the normal case derivative, the differential order in such equations is with a fractional...

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Vydané v:Computers & mathematics with applications (1987) Ročník 73; číslo 6; s. 1243 - 1261
Hlavný autor: Abu Arqub, Omar
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Oxford Elsevier Ltd 15.03.2017
Elsevier BV
Predmet:
(Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker–Planck, Fisher’s, and Newell–Whitehead) equations
Boundary conditions
Chemical reactions
Computer simulation
Elasticity
Exact solutions
Fluid mechanics
Hilbert space
Image acquisition
Mathematical models
Neumann boundary conditions
Partial differential equations
Population growth
Reproducing kernel Hilbert space method
Studies
Time-fractional partial differential equations
Time-fractional partial differential equations
Reproducing kernel Hilbert space method
Neumann boundary conditions
(Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker–Planck, Fisher’s, and Newell–Whitehead) equations
ISSN:0898-1221, 1873-7668
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Popis
Shrnutí:Latterly, many problems arising in different fields of science and engineering can be reduced, by applying some appropriate discretization, to a series of time-fractional partial differential equations. Unlike the normal case derivative, the differential order in such equations is with a fractional order, which will lead to new challenges for numerical simulation. The purpose of this analysis is to introduce the reproducing kernel Hilbert space method for treating classes of time-fractional partial differential equations subject to Neumann boundary conditions with parameters derivative arising in fluid-mechanics, chemical reactions, elasticity, anomalous diffusion, and population growth models. The method provides appropriate representation of the solutions in convergent series formula with accurately computable components. Numerical experiments with different order derivatives degree are performed to support the theoretical analyses which are acquired by interrupting the n-term of the exact solutions. Finally, the obtained outcomes showed that the proposed method is competitive in terms of the quality of the solutions found and is very valid for solving such time-fractional Neumann problems.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2016.11.032