Displaying similar documents to “Weak solutions to differential equations with left and right fractional derivatives defined on ℝ ”

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 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...

Linear Fractional PDE, Uniqueness of Global Solutions

Schäfer, Ingo, Kempfle, Siegmar, Nolte, Bodo (2005)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33, 47A60, 30C15. In this paper we treat the question of existence and uniqueness of solutions of linear fractional partial differential equations. Along examples we show that, due to the global definition of fractional derivatives, uniqueness is only sure in case of global initial conditions.

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.

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...