A novel operational matrix method for solving singularly perturbed boundary value problems of fractional multi-order. Issue 4 (3rd April 2018)

• Record Type: Journal Article
• Authors: Sayevand, K.; Pichaghchi, K.
• Is Part Of: International journal of computer mathematics. Volume 95:Issue 4(2018)
• Page Start: 767
• Page End: 796
• Publication Date: 2018-04-03
• Subjects: Singular perturbation -- Operational matrix -- B-spline -- Caputo fractional derivative -- Boundary value problem; 34A08 -- 41A15 -- 34K26 -- 34K10; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2017.1296574
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this paper, we will consider a wide class of singularly perturbed problems described by the differential equation of fractional multi-order with small parameter multiplying the highest derivative and the appropriate boundary conditions. We construct the linear B-spline operational matrix of fractional derivative in the Caputo sense and introduce a new operational method to solve the mentioned problems. The main characteristic behind this method is that it converts such problems to a system of algebraic equations and overcomes the difficulty and computational complexity induced by the problem. Some illustrative examples are included to demonstrate the validity and applicability of the method.