TY - JOUR
T1 - A Convergent Algorithm for Solving Higher-Order Nonlinear Fractional Boundary Value Problems
AU - Al-Mdallal, Qasem M.
AU - Hajji, Mohamed A.
N1 - Publisher Copyright:
© 2015 Diogenes Co. Sofia.
PY - 2015/12/1
Y1 - 2015/12/1
N2 - We present a numerical algorithm for solving nonlinear fractional boundary value problems of order n, n ∈ IN. The Bernstein polynomials (BPs) are redefined in a fractional form over an arbitrary interval [a, b]. Theoretical results related to the ractional Bernstein polynomials (FBPs) are proven. The well-known shooting technique is extended for the numerical treatment of nonlinear fractional boundary value problems of arbitrary order. The initial value problems were solved using a collocation method with collocation points at the location of the local maximum of the FBPs. Several examples are discussed to illustrate the efficiency and accuracy of the present scheme.
AB - We present a numerical algorithm for solving nonlinear fractional boundary value problems of order n, n ∈ IN. The Bernstein polynomials (BPs) are redefined in a fractional form over an arbitrary interval [a, b]. Theoretical results related to the ractional Bernstein polynomials (FBPs) are proven. The well-known shooting technique is extended for the numerical treatment of nonlinear fractional boundary value problems of arbitrary order. The initial value problems were solved using a collocation method with collocation points at the location of the local maximum of the FBPs. Several examples are discussed to illustrate the efficiency and accuracy of the present scheme.
KW - Caputo's fractional derivative
KW - Fractional Bernstein polynomials
KW - collocation method
KW - shooting method
UR - http://www.scopus.com/inward/record.url?scp=84949806764&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84949806764&partnerID=8YFLogxK
U2 - 10.1515/fca-2015-0082
DO - 10.1515/fca-2015-0082
M3 - Article
AN - SCOPUS:84949806764
SN - 1311-0454
VL - 18
SP - 1423
EP - 1440
JO - Fractional Calculus and Applied Analysis
JF - Fractional Calculus and Applied Analysis
IS - 6
ER -