TY  - EJOU
AU  - Ameen, I. G. 
AU  - Elkot, N. A. 
AU  - Zaky, M. A. 
AU  - Hendy, A. S. 
AU  - Doha, E. H. 

TI  - A Pseudo-Spectral Scheme for Systems of Two-Point Boundary Value Problems with Left and Right Sided Fractional Derivatives and Related Integral Equations
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2021
VL  - 128
IS  - 1
SN  - 1526-1506

AB  - We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving
left- and right-sided fractional derivatives. The main ingredient of the proposed method is to recast the problem
into an equivalent system of weakly singular integral equations. Then, a Legendre-based spectral collocation
method is developed for solving the transformed system. Therefore, we can make good use of the advantages of the
Gauss quadrature rule. We present the construction and analysis of the collocation method. These results can be
indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange
equations. Two numerical examples are given to confirm the convergence analysis and robustness of the scheme.
KW  - Spectral collocation method; weakly singular integral equations; two-point boundary value problems; convergence analysis

DO  - 10.32604/cmes.2021.015310