A note on fractional Sumudu transform.
Gupta, V.G., Shrama, Bhavna, Kiliçman, Adem (2010)
Journal of Applied Mathematics
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Gupta, V.G., Shrama, Bhavna, Kiliçman, Adem (2010)
Journal of Applied Mathematics
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R.K. Saxena, S.L. Bora (1971)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Huang, F. (2009)
Journal of Applied Mathematics
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Li-Li Liu, Jun-Sheng Duan (2015)
Open Mathematics
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In this paper, we investigate the solution of the fractional vibration equation, where the damping term is characterized by means of the Caputo fractional derivative with the order α satisfying 0 < α < 1 or 1 < α < 2. Detailed analysis for the fundamental solution y(t) is carried out through the Laplace transform and its complex inversion integral formula. We conclude that y(t) is ultimately positive, and ultimately decreases monotonically and approaches zero for the case...
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.
N. C. Jain (1970)
Annales Polonici Mathematici
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Boyadjiev, Lyubomir, Al-Saqabi, Bader (2012)
Mathematica Balkanica New Series
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MSC 2010: 35R11, 42A38, 26A33, 33E12 The method of integral transforms based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is utilized for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the Weyl space-fractional operator. The solutions obtained are in integral form whose kernels are Green functions expressed...
Kumar, Dilip, Kilbas, Anatoly (2010)
Fractional Calculus and Applied Analysis
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MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99 The fractional calculus of the P-transform or pathway transform which is a generalization of many well known integral transforms is studied. The Mellin and Laplace transforms of a P-transform are obtained. The composition formulae for the various fractional operators such as Saigo operator, Kober operator and Riemann-Liouville fractional integral and differential operators with P-transform are proved. Application of the P-transform...
Kiryakova, Virginia (2011)
Union of Bulgarian Mathematicians
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Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата. ...
Debnath, Lokenath (2003)
International Journal of Mathematics and Mathematical Sciences
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H. Hövel, U. Westphal (1972)
Studia Mathematica
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Sakhnovich, A.L., Sakhnovich, L.A. (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Nikolova, Yanka, Boyadjiev, Lyubomir (2010)
Fractional Calculus and Applied Analysis
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Mathematical Subject Classification 2010: 35R11, 42A38, 26A33, 33E12. The method of integral transforms based on using a fractional generalization of the Fourier transform and the classical Laplace transform is applied for solving Cauchy-type problem for the time-space fractional diffusion equation expressed in terms of the Caputo time-fractional derivative and a generalized Riemann-Liouville space-fractional derivative.