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.
Karapetyants, N.K., Ginzburg, A.I. (1995)
Georgian Mathematical Journal
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Tijana Levajković, Dora Seleši (2011)
Publications de l'Institut Mathématique
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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...
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...
Çag̃lar, Mert, Polatog̃lu, Yaşar, Yavuz, Emel (2008)
Matematichki Vesnik
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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...
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.
B. Stanković (2008)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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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...