Displaying similar documents to “Existence of solutions for fractional differential inclusions with boundary conditions.”

Fractional Integration and Fractional Differentiation of the M-Series

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...

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

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...

On q–Analogues of Caputo Derivative and Mittag–Leffler Function

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.