Abstract
In this paper we present both main approaches in the interpretation of the impulses in generalized proportional Caputo fractional differential equations. We started with both equivalent interpretations in differential equations with integer order derivatives and based on them we presented both main cases: with fixed lower limit of the fractional derivative at the initial time and with a changeable lower limit at any impulsive time. In both cases we give an integral presentation of teh solution. Several examples illustrate the concepts.
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Acknowledgements
S. H. is partially supported by Plovdiv University under Project FP23-FMI-002, R.T.is partially supported by the Bulgarian National Science Fund under Project KP-06-PN62/1.
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Hristova, S., Terzieva, R. (2024). Impulses in Generalized Proportional Caputo Fractional Differential Equations and Equivalent Integral Presentation. In: Slavova, A. (eds) New Trends in the Applications of Differential Equations in Sciences. NTADES 2023. Springer Proceedings in Mathematics & Statistics, vol 449. Springer, Cham. https://doi.org/10.1007/978-3-031-53212-2_22
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DOI: https://doi.org/10.1007/978-3-031-53212-2_22
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