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

• Published in: Computers & mathematics with applications (1987) Vol. 73; no. 6; pp. 1243 - 1261
• Main Author: Abu Arqub, Omar
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 15.03.2017; Elsevier BV
• Subjects: (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
• DOI: 10.1016/j.camwa.2016.11.032

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.