Displaying similar documents to “On q–Analogues of Caputo Derivative and Mittag–Leffler Function”

Fractional Calculus of the Generalized Wright Function

Kilbas, Anatoly (2005)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33, 33C20. The paper is devoted to the study of the fractional calculus of the generalized Wright function pΨq(z) defined for z ∈ C, complex ai, bj ∈ C and real αi, βj ∈ R (i = 1, 2, · · · p; j = 1, 2, · · · , q) by the series pΨq (z) It is proved that the Riemann-Liouville fractional integrals and derivative of the Wright function are also the Wright functions but of greater order. Special cases are considered. * The present...

An Expansion Formula for Fractional Derivatives and its Application

Atanackovic, T., Stankovic, B. (2004)

Fractional Calculus and Applied Analysis

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An expansion formula for fractional derivatives given as in form of a series involving function and moments of its k-th derivative is derived. The convergence of the series is proved and an estimate of the reminder is given. The form of the fractional derivative given here is especially suitable in deriving restrictions, in a form of internal variable theory, following from the second law of thermodynamics, when applied to linear viscoelasticity of fractional derivative type. ...

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...

On the Operational Solution of a System of Fractional Differential Equations

Takači, Dj., Takači, A. (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 44A45, 44A40, 65J10 We consider a linear system of differential equations with fractional derivatives, and its corresponding system in the field of Mikusiński operators, written in a matrix form, by using the connection between the fractional and the Mikusiński calculus. The exact and the approximate operational solution of the corresponding matrix equations, with operator entries are determined, and their characters are analyzed. By using the packages...

On Integral Means for Fractional Calculus Operators of Multivalent Functions

Sümer Eker, S., Özlem Güney, H., Owa, Shigeyoshi (2006)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: Primary 30C45, Secondary 26A33, 30C80 Integral means inequalities are obtained for the fractional derivatives and the fractional integrals of multivalent functions. Relevant connections with various known integral means inequalities are also pointed out.

On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function

Kalla, S., Yadav, R., Purohit, S. (2005)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 33D60, 26A33, 33C60 The present paper envisages the applications of Riemann-Liouville fractional q-integral operator to a basic analogue of Fox H-function. Results involving the basic hypergeometric functions like Gq(.), Jv(x; q), Yv(x; q),Kv(x; q), Hv(x; q) and various other q-elementary functions associated with the Riemann-Liouville fractional q-integral operator have been deduced as special cases of the main result.

Fractional Integration of the Product of Bessel Functions of the First Kind

Kilbas, Anatoly, Sebastian, Nicy (2010)

Fractional Calculus and Applied Analysis

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Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09 Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for...