TY - JOUR
T1 - An efficient method for solving non-linear singularly perturbed two points boundary-value problems of fractional order
AU - Al-Mdallal, Qasem M.
AU - Syam, Muhammed I.
N1 - Funding Information:
The authors would like to express their appreciation for the valuable comments of the reviewers. The authors also would like to express their sincere appreciation to the United Arab Emirates University Research Affairs for the financial support of Grant No. 1643-02-01-10 .
PY - 2012/6
Y1 - 2012/6
N2 - In this paper, we discuss a numerical solution of a class of non-linear fractional singularly perturbed two points boundary-value problem. The method of solution consists of solving reduced problem and boundary layer correction problem. A series method is used to solve the boundary layer correction problem, and then the series solutions is approximated by the Pade' approximant of order [m, m]. Some theoretical results are established and proved. Two numerical examples are discussed to illustrate the efficiency of the present scheme.
AB - In this paper, we discuss a numerical solution of a class of non-linear fractional singularly perturbed two points boundary-value problem. The method of solution consists of solving reduced problem and boundary layer correction problem. A series method is used to solve the boundary layer correction problem, and then the series solutions is approximated by the Pade' approximant of order [m, m]. Some theoretical results are established and proved. Two numerical examples are discussed to illustrate the efficiency of the present scheme.
KW - Boundary layer
KW - Boundary layer correction
KW - Fractional derivative
KW - Pade' approximation
KW - Singularly perturbed boundary-value problems
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U2 - 10.1016/j.cnsns.2011.10.003
DO - 10.1016/j.cnsns.2011.10.003
M3 - Article
AN - SCOPUS:84855251712
SN - 1007-5704
VL - 17
SP - 2299
EP - 2308
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
IS - 6
ER -