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Hamani, Samira, Benchohra, Mouffak, Graef, John R. (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Atmania, Rahima, Mazouzi, Said (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Benchohra, Mouffak, Hamani, Samira, Nieto, Juan Jose, Slimani, Boualem Attou (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Zhang, Shuqin (2006)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Sharma, Manoj (2008)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33, 33C60, 44A15 In this paper a new special function called as M-series is introduced. This series is a particular case of the H-function of Inayat-Hussain. The M-series is interesting because the pFq -hypergeometric function and the Mittag-Leffler function follow as its particular cases, and these functions have recently found essential applications in solving problems in physics, biology, engineering and applied sciences. Let us note...
Su, Xinwei, Zhang, Shuqin (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Luchko, Yury, Trujillo, Juan (2007)
Fractional Calculus and Applied Analysis
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2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05 The Caputo fractional derivative is one of the most used definitions of a fractional derivative along with the Riemann-Liouville and the Grünwald- Letnikov ones. Whereas the Riemann-Liouville definition of a fractional derivative is usually employed in mathematical texts and not so frequently in applications, and the Grünwald-Letnikov definition – for numerical approximation of both Caputo and Riemann-Liouville...
Abbas, Said, Agarwal, Ravi P., Benchohra, Mouffak (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Ibrahim, Rabha W. (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Rajkovic, Predrag, Marinkovic, Sladjana, Stankovic, Miomir (2007)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 33D60, 33E12, 26A33 Based on the fractional q–integral with the parametric lower limit of integration, we consider the fractional q–derivative of Caputo type. Especially, its applications to q-exponential functions allow us to introduce q–analogues of the Mittag–Leffler function. Vice versa, those functions can be used for defining generalized operators in fractional q–calculus.
Yuan, Chengjun (2010)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Saxena, R. K., Saigo, Megumi (2005)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33, 33E12, 33C20. It has been shown that the fractional integration and differentiation operators transform such functions with power multipliers into the functions of the same form. Some of the results given earlier by Kilbas and Saigo follow as special cases.