A class of nonlinear differential equations with fractional integrable impulses |
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| Affiliation: | 1. School of Mathematics and Computer Science, Guizhou Normal College, Guiyang, Guizhou 550018, PR China;2. Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, PR China;1. School of Mathematical Sciences/Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China;2. Department of Mathematics and Computer Science, Anshun University, Anshun, Guizhou 561000, PR China;1. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland;3. Nonlinear Analysis and Applied Mathematics, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;1. Department of Higher Mathematics, Voronezh State Pedagogical University, 394043, Voronezh, Russian Federation;2. Voronezh State University, 394018, Voronezh, Russian Federation;3. Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan |
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| Abstract: | In this paper, we introduce a new class of impulsive differential equations, which is more suitable to characterize memory processes of the drugs in the bloodstream and the consequent absorption for the body. This fact offers many difficulties in applying the usual methods to analysis and novel techniques in Bielecki’s normed Banach spaces and thus makes the study of existence and uniqueness theorems interesting. Meanwhile, new concepts of Bielecki–Ulam’s type stability are introduced and generalized Ulam–Hyers–Rassias stability results on a compact interval are established. This is another novelty of this paper. Finally, an interesting example is given to illustrate our theory results. |
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| Keywords: | Impulsive differential equations Solutions Bielecki–Ulam’s type stability |
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