Characterization properties for starlike and convex functions involving a class of fractional integral operators
R. K. Raina, Mamta Bolia (1997)
Rendiconti del Seminario Matematico della Università di Padova
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R. K. Raina, Mamta Bolia (1997)
Rendiconti del Seminario Matematico della Università di Padova
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Atici, F.M., Eloe, P. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Daftardar-Gejji, Varsha, Bhalekar, Sachin (2008)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33, 31B10 In the present paper a New Iterative Method [1] has been employed to find solutions of linear and non-linear fractional diffusion-wave equations. Illustrative examples are solved to demonstrate the efficiency of the method. * This work has partially been supported by the grant F. No. 31-82/2005(SR) from the University Grants Commission, N. Delhi, India.
Tadeusz Kaczorek (2008)
International Journal of Applied Mathematics and Computer Science
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A new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems.
Samuel, M., Thomas, Anitha (2010)
Fractional Calculus and Applied Analysis
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MSC 2010: 26A33, 33E12, 33C60, 35R11 In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox's H-function.
R.K. Raina, Mamta Bolia (1998)
Annales mathématiques Blaise Pascal
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Atanackovic, Teodor, Stankovic, Bogoljub (2007)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05 We treat the fractional order differential equation that contains the left and right Riemann-Liouville fractional derivatives. Such equations arise as the Euler-Lagrange equation in variational principles with fractional derivatives. We reduce the problem to a Fredholm integral equation and construct a solution in the space of continuous functions. Two competing approaches in formulating differential equations...
Krishnan Balachandran, Jayakumar Kokila (2012)
International Journal of Applied Mathematics and Computer Science
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This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder's fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.