Solution operators of three time variables for fractional linear problems |
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| Authors: | Hassan Emamirad Arnaud Rougirel |
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| Affiliation: | 1. Laboratoire de Mathématiques, Université de Poitiers, Chassneuil du Poitou, Cedex, France;2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran |
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| Abstract: | It is well known that the time fractional equation  where  is the fractional time derivative in the sense of Caputo of u does not generate a dynamical system in the standard sense. In this paper, we study the algebraic properties of the solution operator T(t,s,τ) for that equation with u(s) = v. We apply this theory to linear time fractional PDEs with constant coefficients. These equations are solved by the Fourier multiplier techniques. It appears that their solution exhibits some singularity, which leads us to introduce a new kind of solution for abstract time fractional problems. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | fractional derivatives solution operators |
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where 
is the fractional time derivative in the sense of Caputo of u does not generate a dynamical system in the standard sense. In this paper, we study the algebraic properties of the solution operator T(t,s,τ) for that equation with u(s) = v. We apply this theory to linear time fractional PDEs with constant coefficients. These equations are solved by the Fourier multiplier techniques. It appears that their solution exhibits some singularity, which leads us to introduce a new kind of solution for abstract time fractional problems. Copyright © 2016 John Wiley & Sons, Ltd.