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Pseudo-almost periodic solutions of a class of semilinear fractional differential equations |
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| Authors: | Ravi P Agarwal Claudio Cuevas Herme Soto |
| Institution: | 1. Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL, 32901, USA 2. Departamento de Matemática, Universidade Federal de Pernambuco, Recife, PE, 50540-740, Brazil 3. Departamento de Matemática y Estadística, Universidad de La Frontera, Casilla 54-D, Temuco, Chile |
| Abstract: | We study existence and uniqueness of a pseudo-almost periodic (of class infinity) mild solution to the semilinear fractional equation $\partial_{t}^{\alpha}u=Au+\partial_{t}^{\alpha-1}f(\cdot,u),1<\alpha<2$ , where A is a linear operator of sectorial negative type. |
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