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Extremal solutions of Cauchy problems for abstract fractional differential equations |
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| Authors: | JinRong Wang Yong Zhou Milan Medveď |
| Affiliation: | 1. School of Mathematics and Computer Science, Guizhou Normal College Guiyang, 550018, Guizhou, China 2. Department of Mathematics, Xiangtan University Xiangtan, 411105, Hunan, China 3. Department of Mathematical and Numerical Mathematics, Comenius University Bratislava, SK-842 15, Bratislava, Slovakia |
| Abstract: | In this paper, we study the extremal solutions of Cauchy problems for abstract fractional differential equations. Some definitions such as L 1-Lipschitz-like, L 1-Carathéodory-like and L 1-Chandrabhan-like are introduced. By virtue of the singular integral inequalities with several nonlinearities due to Medved’, the properties of solutions are given. By using a hybrid fixed point theorem due to Dhage, existence results for extremal solutions are established. Finally, we present an example to illustrate our main results. |
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