COLLOCATION BASED APPROXIMATIONS FOR A CLASS OF FRACTIONAL BOUNDARY VALUE PROBLEMS

A boundary value problem for fractional integro-differential equations with weakly singular kernels is considered. The reformulated as an integral equation of the second kind respect to, Caputo derivative y order α, 1 < α 2, where solution original problem. Using this reformulation, regularity properties both and its z are studied. Based on information a piecewise polynomial collocation method developed finding approximate zN zN, approximation yN constructed detailed convergence analysis proposed given. In particular, attainable appropriate values grid parameters established. To illustrate performance our approach, results some numerical experiments presented.