Series Solution of the Pantograph Equation and Its Properties
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 relati...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2017-12-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/1/1/16 |
| _version_ | 1818620967250821120 |
|---|---|
| author | Sachin Bhalekar Jayvant Patade |
| author_facet | Sachin Bhalekar Jayvant Patade |
| author_sort | Sachin Bhalekar |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-16T18:01:47Z |
| format | Article |
| id | doaj.art-9e1d467b17454d83b8909a6ecbff6c35 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-12-16T18:01:47Z |
| publishDate | 2017-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-9e1d467b17454d83b8909a6ecbff6c352022-12-21T22:22:02ZengMDPI AGFractal and Fractional2504-31102017-12-01111610.3390/fractalfract1010016fractalfract1010016Series Solution of the Pantograph Equation and Its PropertiesSachin Bhalekar0Jayvant Patade1Department of Mathematics, Shivaji University, Kolhapur 416004, IndiaDepartment of Mathematics, Shivaji University, Kolhapur 416004, IndiaIn 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.https://www.mdpi.com/2504-3110/1/1/16pantograph equationproportional delayfractional derivativeGaussian binomial coefficient |
| spellingShingle | Sachin Bhalekar Jayvant Patade Series Solution of the Pantograph Equation and Its Properties Fractal and Fractional pantograph equation proportional delay fractional derivative Gaussian binomial coefficient |
| title | Series Solution of the Pantograph Equation and Its Properties |
| title_full | Series Solution of the Pantograph Equation and Its Properties |
| title_fullStr | Series Solution of the Pantograph Equation and Its Properties |
| title_full_unstemmed | Series Solution of the Pantograph Equation and Its Properties |
| title_short | Series Solution of the Pantograph Equation and Its Properties |
| title_sort | series solution of the pantograph equation and its properties |
| topic | pantograph equation proportional delay fractional derivative Gaussian binomial coefficient |
| url | https://www.mdpi.com/2504-3110/1/1/16 |
| work_keys_str_mv | AT sachinbhalekar seriessolutionofthepantographequationanditsproperties AT jayvantpatade seriessolutionofthepantographequationanditsproperties |