Abstract
Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay, depending on both the time and the state variable. The case when the lower limit of the Caputo fractional derivative is fixed at the initial time, and the case when the lower limit of the fractional derivative is changed at the end of each interval of action of the impulse are studied. Practical stability properties, based on the modified Razumikhin method are investigated. Several examples are given in this paper to illustrate the results.
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R. Almeida was supported by Portuguese funds through the CIDMA — Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), within project UIDB/04106/2020, and Fund Scientific Research MU21FMI007, University of Plovdiv “Paisii Hilendarski”.
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Agarwal, R., Almeida, R., Hristova, S. et al. Non-Instantaneous Impulsive Fractional Differential Equations with State Dependent Delay and Practical Stability. Acta Math Sci 41, 1699–1718 (2021). https://doi.org/10.1007/s10473-021-0518-1
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DOI: https://doi.org/10.1007/s10473-021-0518-1