A novel operational matrix method for solving singularly perturbed boundary value problems of fractional multi-order

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.

KEYWORDS:

• Singular perturbation
• Operational matrix
• B-spline
• Caputo fractional derivative
• Boundary value problem

2010 AMS SUBJECT CLASSIFICATIONS:

• 34A08
• 41A15
• 34K26
• 34K10

Acknowledgements

We are obliged to the editor and anonymous reviewers of the IJCM for their valuable comments which helped us improve the quality of the initial draft of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.