Quadratic spline solution for boundary value problem of fractional order

Authors:
Waheed K. Zahra;Samah M. Elkholy
Affiliations:
Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt;Department of Engineering Physics and Mathematics, Faculty of Engineering, Kafr El Sheikh University, Kafr El Sheikh, Egypt
Venue:
Numerical Algorithms
Year:
2012

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Abstract

Fractional differential equations are widely applied in physics, chemistry as well as engineering fields. Therefore, approximating the solution of differential equations of fractional order is necessary. We consider the quadratic polynomial spline function based method to find approximate solution for a class of boundary value problems of fractional order. We derive a consistency relation which can be used for computing approximation to the solution for this class of boundary value problems. Convergence analysis of the method is discussed. Four numerical examples are included to illustrate the practical usefulness of the proposed method.