Existence and numerical simulation of solutions for nonlinear fractional pantograph equations

ABSTRACT

In this paper a method based on Sinc approximation is developed for the numerical solution of a nonlinear fractional pantograph equation. In order to use Sinc approximation, the problem needs to have an analytic solution. So we investigated the existence and uniqueness of analytic solutions in the proposed domain. Single and double exponential transformations are used to approximate the solution. Some test problems are given to demonstrate the efficiency and applicability of the methods. The results are compared with some other existing numerical methods to show the performance and good accuracy of the methods. The numerical orders of convergence show that the method has exponential rate of convergence.

KEYWORDS:

• Fractional pantograph equation
• existence of solution
• sinc approximation
• exponential rate of convergence
• analytic solution

Classification:

• 34A08
• 65M70
• 34A12

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

M. Ghasemi http://orcid.org/0000-0003-0068-0707

J. J. Trujillo http://orcid.org/0000-0001-8700-6410

Additional information

Funding

The third author was partially supported by FEDER and by projects MTM2013-41704-P from the government of Spain.