Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series
Fractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo’s fractional integral operators involving hypergeometric function in the...
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MDPI AG
2019-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/2/206 |
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doaj-388bcb22eacb4ddfb42f4921a841c6d22020-11-24T20:48:14ZengMDPI AGMathematics2227-73902019-02-017220610.3390/math7020206math7020206Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu SeriesK.S. Nisar0D.L. Suthar1M. Bohra2S.D. Purohit3Department of Mathematics, College of Arts & Science-Wadi Al-Dawaser, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi ArabiaDepartment of Mathematics, Wollo University, Dessie 1145, EthiopiaDepartment of Mathematics, Govt. Mahila Engg. College, Ajmer 305001, IndiaDepartment of HEAS (Mathematics), Rajasthan Technical University, Kota 324010, IndiaFractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo’s fractional integral operators involving hypergeometric function in the kernel are applied to the product of Srivastava’s polynomials and the generalized Mathieu series, containing the factor <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>x</mi> <mi>λ</mi> </msup> <msup> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mi>k</mi> </msup> <mo>+</mo> <msup> <mi>c</mi> <mi>k</mi> </msup> <mo>)</mo> </mrow> <mrow> <mo>−</mo> <mi>ρ</mi> </mrow> </msup> </mrow> </semantics> </math> </inline-formula> in its argument. The results are expressed in terms of the generalized hypergeometric function and Hadamard product of the generalized Mathieu series. Corresponding special cases related to the Riemann⁻Liouville and Erdélyi⁻Kober fractional integral operators are also considered.https://www.mdpi.com/2227-7390/7/2/206generalized fractional integral operatorsgeneralized Mathieu seriesSrivastava’s polynomialgeneralized hypergeometric series |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
K.S. Nisar D.L. Suthar M. Bohra S.D. Purohit |
| spellingShingle |
K.S. Nisar D.L. Suthar M. Bohra S.D. Purohit Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series Mathematics generalized fractional integral operators generalized Mathieu series Srivastava’s polynomial generalized hypergeometric series |
| author_facet |
K.S. Nisar D.L. Suthar M. Bohra S.D. Purohit |
| author_sort |
K.S. Nisar |
| title |
Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series |
| title_short |
Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series |
| title_full |
Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series |
| title_fullStr |
Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series |
| title_full_unstemmed |
Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series |
| title_sort |
generalized fractional integral operators pertaining to the product of srivastava’s polynomials and generalized mathieu series |
| publisher |
MDPI AG |
| series |
Mathematics |
| issn |
2227-7390 |
| publishDate |
2019-02-01 |
| description |
Fractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo’s fractional integral operators involving hypergeometric function in the kernel are applied to the product of Srivastava’s polynomials and the generalized Mathieu series, containing the factor <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>x</mi> <mi>λ</mi> </msup> <msup> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mi>k</mi> </msup> <mo>+</mo> <msup> <mi>c</mi> <mi>k</mi> </msup> <mo>)</mo> </mrow> <mrow> <mo>−</mo> <mi>ρ</mi> </mrow> </msup> </mrow> </semantics> </math> </inline-formula> in its argument. The results are expressed in terms of the generalized hypergeometric function and Hadamard product of the generalized Mathieu series. Corresponding special cases related to the Riemann⁻Liouville and Erdélyi⁻Kober fractional integral operators are also considered. |
| topic |
generalized fractional integral operators generalized Mathieu series Srivastava’s polynomial generalized hypergeometric series |
| url |
https://www.mdpi.com/2227-7390/7/2/206 |
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