An equation in the left and right fractional derivatives of the same order
B. Stanković (2008)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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B. Stanković (2008)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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Karapetyants, N.K., Ginzburg, A.I. (1995)
Georgian Mathematical Journal
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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...
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...
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. ...
T. M. Atanacković, S. Pilipović, B. Stanković (2009)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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Wang, Taige, Xie, Feng (2008)
The Journal of Nonlinear Sciences and its Applications
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Da Silva, J. L., Erraoui, M., Ouerdiane, H. (2007)
Fractional Calculus and Applied Analysis
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2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20 In this paper we study the generalized Riemann-Liouville (resp. Caputo) time fractional evolution equation in infinite dimensions. We show that the explicit solution is given as the convolution between the initial condition and a generalized function related to the Mittag-Leffler function. The fundamental solution corresponding to the Riemann-Liouville time fractional evolution equation does...
Benchohra, M., Henderson, J., Ntouyas, S. K., Ouahab, A. (2008)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33, 34A60, 34K40, 93B05 In this paper we investigate the existence of solutions for fractional functional differential inclusions with infinite delay. In the last section we present an application of our main results in control theory.
Qiu, Tingting, Bai, Zhanbing (2008)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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