On the generalized fractional integrals of the generalized Mittag-Leffler function
In this paper, we employ the generalized fractional calculus operators on the generalized Mittag-Leffler function. Some results associated with generalized Wright function are obtained. Recent results of Chaurasia and Pandey are obtained as special cases. 2000 Mathematics Subject Classification 33C4...
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| Published in | SpringerPlus Vol. 3; no. 1; pp. 198 - 5 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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Cham
Springer International Publishing
22.04.2014
Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 2193-1801 2193-1801 |
| DOI | 10.1186/2193-1801-3-198 |
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| Abstract | In this paper, we employ the generalized fractional calculus operators on the generalized Mittag-Leffler function. Some results associated with generalized Wright function are obtained. Recent results of Chaurasia and Pandey are obtained as special cases.
2000 Mathematics Subject Classification
33C45, 47G20, 26A33 |
|---|---|
| AbstractList | In this paper, we employ the generalized fractional calculus operators on the generalized Mittag-Leffler function. Some results associated with generalized Wright function are obtained. Recent results of Chaurasia and Pandey are obtained as special cases.ABSTRACTIn this paper, we employ the generalized fractional calculus operators on the generalized Mittag-Leffler function. Some results associated with generalized Wright function are obtained. Recent results of Chaurasia and Pandey are obtained as special cases.33C45, 47G20, 26A33.2000 MATHEMATICS SUBJECT CLASSIFICATION33C45, 47G20, 26A33. In this paper, we employ the generalized fractional calculus operators on the generalized Mittag-Leffler function. Some results associated with generalized Wright function are obtained. Recent results of Chaurasia and Pandey are obtained as special cases. 2000 Mathematics Subject Classification: 33C45, 47G20, 26A33 In this paper, we employ the generalized fractional calculus operators on the generalized Mittag-Leffler function. Some results associated with generalized Wright function are obtained. Recent results of Chaurasia and Pandey are obtained as special cases. 33C45, 47G20, 26A33. In this paper, we employ the generalized fractional calculus operators on the generalized Mittag-Leffler function. Some results associated with generalized Wright function are obtained. Recent results of Chaurasia and Pandey are obtained as special cases. 2000 Mathematics Subject Classification 33C45, 47G20, 26A33 Abstract In this paper, we employ the generalized fractional calculus operators on the generalized Mittag-Leffler function. Some results associated with generalized Wright function are obtained. Recent results of Chaurasia and Pandey are obtained as special cases. 2000 Mathematics Subject Classification 33C45, 47G20, 26A33 |
| ArticleNumber | 198 |
| Author | Ahmed, Shakeel |
| Author_xml | – sequence: 1 givenname: Shakeel surname: Ahmed fullname: Ahmed, Shakeel email: shakeelamu81@gmail.com organization: Department of Applied Mathematics, Faculty of Engineering, Aligarh Muslim University |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/25674449$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1007/BF02403202 10.1098/rsta.1940.0002 10.1080/10652460310001600717 10.1093/qmath/os-11.1.36 10.1112/plms/s2-46.1.389 10.1112/jlms/s1-10.40.286 |
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| Copyright | Ahmed; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. SpringerPlus is a copyright of Springer, 2014. Ahmed; licensee Springer. 2014 |
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| Keywords | Generalized Mittag-Leffler Function Generalized wright function Generalized fractional calculus operators |
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| References | Chaurasia, Pandey (CR1) 2010; 20 Srivastava, Karlsson (CR10) 1985 (CR16) 1940c; 11 Kilbas, Saigo, Saxena (CR4) 2004; 15 Prabhakar (CR6) 1971; 19 Samko, Kilbas, Marichev (CR9) 1993 (CR14) 1940a; 46 Mittag-Leffler (CR5) 1903; 137 (CR13) 1935; 10 Kilbas, Saigo, Trujillo (CR3) 2002; 5 Erdlyi, Magnus, Oberhettinger, Tricomy (CR2) 1953 Saigo (CR8) 1978; 11 Wiman (CR11) 1905; 29 Rainville (CR7) 1960 Wright (CR12) 1934; 38 (CR15) 1940b; 238 AA Kilbas (1475_CR3) 2002; 5 AA Kilbas (1475_CR4) 2004; 15 SG Samko (1475_CR9) 1993 EM Wright (1475_CR12) 1934; 38 M Saigo (1475_CR8) 1978; 11 VBL Chaurasia (1475_CR1) 2010; 20 A Erdlyi (1475_CR2) 1953 ED Rainville (1475_CR7) 1960 Wright, EM (1475_CR16) 1940c; 11 Wright, EM (1475_CR14) 1940a; 46 GM Mittag-Leffler (1475_CR5) 1903; 137 HM Srivastava (1475_CR10) 1985 Wright, EM (1475_CR13) 1935; 10 Wright, EM (1475_CR15) 1940b; 238 A Wiman (1475_CR11) 1905; 29 TR Prabhakar (1475_CR6) 1971; 19 |
| References_xml | – year: 1953 ident: CR2 publication-title: Higher transcendental functions – volume: 10 start-page: 286 year: 1935 end-page: 293 ident: CR13 article-title: The asymptotic expansion of generalized hypergeometric functions publication-title: J London Math Soc – volume: 19 start-page: 7 year: 1971 end-page: 15 ident: CR6 article-title: A singular integral equation with a generalized Mittag-Leffler function in the kernel publication-title: Yokohama Math J – volume: 20 start-page: 113 year: 2010 end-page: 122 ident: CR1 article-title: On the fractional calculus of generalized Mittag-Leffler function publication-title: Scientia, Ser A; Math Sci – volume: 137 start-page: 554 year: 1903 end-page: 558 ident: CR5 article-title: Sur la nouvelle fonction ( ) publication-title: C R Acad Sci Paris – year: 1985 ident: CR10 publication-title: Multiple Gaussian hypergeometric series – volume: 11 start-page: 135 year: 1978 end-page: 143 ident: CR8 article-title: A remark on integral operators involving the Gauss hypergeometric functions publication-title: Math Rep Kyushu Univ – volume: 29 start-page: 191 year: 1905 end-page: 201 ident: CR11 article-title: Uber den fundamental Satz in der Theorie der Funktionen ( ) publication-title: Acta Math doi: 10.1007/BF02403202 – volume: 238 start-page: 423 year: 1940b end-page: 445 ident: CR15 article-title: The asymptotic expansion of integral functions defined by Taylor series publication-title: Philos Trans Roy Soc London, Ser A doi: 10.1098/rsta.1940.0002 – year: 1960 ident: CR7 publication-title: Special functions – volume: 5 start-page: 437 issue: 4 year: 2002 end-page: 460 ident: CR3 article-title: On the generalized Wright function publication-title: Frac Calc Apl Anal – volume: 15 start-page: 31 year: 2004 end-page: 49 ident: CR4 article-title: Generalized Mittag-Leffler function and generalized fractional calculus operators publication-title: Integral Transforms Spec Funct doi: 10.1080/10652460310001600717 – year: 1993 ident: CR9 publication-title: Fractional integrals and derivatives: theory and applications – volume: 11 start-page: 36 year: 1940c end-page: 48 ident: CR16 article-title: The generalized Bessel function of order greater than one publication-title: Quart J Math Oxford Ser doi: 10.1093/qmath/os-11.1.36 – volume: 38 start-page: 257 issue: 2 year: 1934 end-page: 270 ident: CR12 article-title: The asymptotic expansion of generalized Bessel function publication-title: Proc London Math Soc – volume: 46 start-page: 389 issue: 2 year: 1940a end-page: 408 ident: CR14 article-title: The asymptotic expansion of generalized hypergeometric functions publication-title: J London Math Soc doi: 10.1112/plms/s2-46.1.389 – volume-title: Multiple Gaussian hypergeometric series year: 1985 ident: 1475_CR10 – volume: 137 start-page: 554 year: 1903 ident: 1475_CR5 publication-title: C R Acad Sci Paris – volume: 15 start-page: 31 year: 2004 ident: 1475_CR4 publication-title: Integral Transforms Spec Funct doi: 10.1080/10652460310001600717 – volume: 38 start-page: 257 issue: 2 year: 1934 ident: 1475_CR12 publication-title: Proc London Math Soc – volume: 29 start-page: 191 year: 1905 ident: 1475_CR11 publication-title: Acta Math doi: 10.1007/BF02403202 – volume-title: Special functions year: 1960 ident: 1475_CR7 – volume: 20 start-page: 113 year: 2010 ident: 1475_CR1 publication-title: Scientia, Ser A; Math Sci – volume-title: Higher transcendental functions year: 1953 ident: 1475_CR2 – volume-title: Fractional integrals and derivatives: theory and applications year: 1993 ident: 1475_CR9 – volume: 19 start-page: 7 year: 1971 ident: 1475_CR6 publication-title: Yokohama Math J – volume: 5 start-page: 437 issue: 4 year: 2002 ident: 1475_CR3 publication-title: Frac Calc Apl Anal – volume: 11 start-page: 135 year: 1978 ident: 1475_CR8 publication-title: Math Rep Kyushu Univ – volume: 10 start-page: 286 year: 1935 ident: 1475_CR13 publication-title: J London Math Soc doi: 10.1112/jlms/s1-10.40.286 – volume: 46 start-page: 389 issue: 2 year: 1940a ident: 1475_CR14 publication-title: J London Math Soc doi: 10.1112/plms/s2-46.1.389 – volume: 11 start-page: 36 year: 1940c ident: 1475_CR16 publication-title: Quart J Math Oxford Ser doi: 10.1093/qmath/os-11.1.36 – volume: 238 start-page: 423 year: 1940b ident: 1475_CR15 publication-title: Philos Trans Roy Soc London, Ser A doi: 10.1098/rsta.1940.0002 |
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| Title | On the generalized fractional integrals of the generalized Mittag-Leffler function |
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