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2024 | OriginalPaper | Chapter

Impulses in Generalized Proportional Caputo Fractional Differential Equations and Equivalent Integral Presentation

Authors : Snezhana Hristova, Radoslava Terzieva

Published in: New Trends in the Applications of Differential Equations in Sciences

Publisher: Springer Nature Switzerland

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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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previous chapter Numerous Exact Solutions of the Wu-Zhang System with Conformable Time–Fractional Derivatives via Simple Equations Method (SEsM): The Case of Two Simple Equations

next chapter Reconstruction of the Time-Dependent Diffusion Coefficient in a Space-Fractional Parabolic Equation

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Title: Impulses in Generalized Proportional Caputo Fractional Differential Equations and Equivalent Integral Presentation
Authors: Snezhana Hristova
Radoslava Terzieva
Publisher: Springer Nature Switzerland
Book: New Trends in the Applications of Differential Equations in Sciences
Print ISBN: 978-3-031-53211-5

Electronic ISBN: 978-3-031-53212-2

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-53212-2_22

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