Approximate solution of linear and nonlinear fractional differential equations under m-point local and nonlocal boundary conditions

Advances in Difference Equations

Dumitru Baleanu¹  Samir H Saker²  Rahmat Ali Khan³  Hammad Khalil⁴ 

[1] Dean Faculty of Science, University of Malakand, Chakdara, Dir Lower, Pakistan;Department of Mathematics and Computer Science, Cankaya University, Ankara, Turkey;Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Pakistan;Department of Mathematics, University of Poonch Rawalakot, Rawalakot, Pakistan

关键词: Bernstein polynomials;    operational matrices;    m-point boundary conditions;    fractional differential equations;    35C11;    65T99;   

DOI  :  10.1186/s13662-016-0910-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper investigates a computational method to find an approximation to the solution of fractional differential equations subject to local and nonlocal m-point boundary conditions. The method that we will employ is a variant of the spectral method which is based on the normalized Bernstein polynomials and its operational matrices. Operational matrices that we will developed in this paper have the ability to convert fractional differential equations together with its nonlocal boundary conditions to a system of easily solvable algebraic equations. Some test problems are presented to illustrate the efficiency, accuracy, and applicability of the proposed method.

【 授权许可】

CC BY