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Fractal Fract 2017, 1(1), 16; doi:10.3390/fractalfract1010016

Series Solution of the Pantograph Equation and Its Properties

Department of Mathematics, Shivaji University, Kolhapur 416004, India
Ashokrao Mane Group of Institution, Vathar, Kolhapur 416112, India
Author to whom correspondence should be addressed.
Received: 26 October 2017 / Revised: 28 November 2017 / Accepted: 30 November 2017 / Published: 8 December 2017
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering)
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In this paper, we discuss the classical pantograph equation and its generalizations to include fractional order and the higher order case. The special functions are obtained from the series solution of these equations. We study different properties of these special functions and establish the relation with other functions. Further, we discuss some contiguous relations for these special functions. View Full-Text
Keywords: pantograph equation; proportional delay; fractional derivative; Gaussian binomial coefficient pantograph equation; proportional delay; fractional derivative; Gaussian binomial coefficient

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Bhalekar, S.; Patade, J. Series Solution of the Pantograph Equation and Its Properties. Fractal Fract 2017, 1, 16.

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