Existence of solutions for nonlinear Caputo-Hadamard fractional differential equations via the method of upper and lower solutions
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Authors
Yunru Bai
- Institute of Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Lojasiewicza 6, 30-348 Krakow, Poland.
- Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, China.
Hua Kong
- Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, China.
Abstract
The purpose of this paper is devoted to consider the existence of solutions for a class of nonlinear Caputo-Hadamard fractional differential equations with integral terms ((CHFDE), for short). Firstly, by applying the semi-group property of Hadamard fractional integral operator, a necessary condition of solvability for (CHFDE) is established. Then, under the suitable conditions, we prove the solution set of (CHFDE) is nonempty by using the method of upper and lower solutions, and Arzel\`{a}-Ascoli theorem. Finally, we present several numerical examples to explicate
the main results.
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ISRP Style
Yunru Bai, Hua Kong, Existence of solutions for nonlinear Caputo-Hadamard fractional differential equations via the method of upper and lower solutions, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 11, 5744--5752
AMA Style
Bai Yunru, Kong Hua, Existence of solutions for nonlinear Caputo-Hadamard fractional differential equations via the method of upper and lower solutions. J. Nonlinear Sci. Appl. (2017); 10(11):5744--5752
Chicago/Turabian Style
Bai, Yunru, Kong, Hua. "Existence of solutions for nonlinear Caputo-Hadamard fractional differential equations via the method of upper and lower solutions." Journal of Nonlinear Sciences and Applications, 10, no. 11 (2017): 5744--5752
Keywords
- Caputo-Hadamard derivative
- fractional differential equations
- upper and lower solutions
- monotone sequences
- Arzela-Ascoli theorem
MSC
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