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Open AccessArticle

Series Solution of the Pantograph Equation and Its Properties

1
Department of Mathematics, Shivaji University, Kolhapur 416004, India
2
Ashokrao Mane Group of Institution, Vathar, Kolhapur 416112, India
*
Author to whom correspondence should be addressed.
Fractal Fract 2017, 1(1), 16; https://doi.org/10.3390/fractalfract1010016
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)
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
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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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