An exponential spline technique for solving fractional boundary value problem

作者：Akram Ghazala^*; Tariq Hira

来源：Calcolo, 2016, 53(4): 545-558.

DOI：10.1007/s10092-015-0161-0

• Boundary value problem
• Exponential spline function
• Caputo's fractional operators
• Error bound

Differential equations of fractional order are widely used in physics, chemistry as well as engineering fields, this is the main reason that the approximate solution of fractional differential equations becomes a hot topic. In this paper, a numerical scheme for a class of fractional boundary value problems ( FBVPs) is presented. In this approach, the FBVPs are expressed in terms of Caputo's fractional derivative. This scheme is based on exponential spline functions consisting of a polynomial part of degree one and an exponential part. For convergence analysis of this method, it is assumed that the exact solution of fractional boundary value problem belongs to a class of C-6-functions. Numerical examples are considered to illustrate the practical usefulness of this method and comparison show that this scheme is more accurate than the existing method Zahra and Elkholy ( Numer Algorithms 59: 373-391, 2012).

• 出版日期2016-12