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Non-Instantaneous Impulses in Differential Equations

Donal O'Regan, Snezhana Hristova, Ravi Agarwal, et al.

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Springer International Publishing img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Analysis

Beschreibung

This monograph is the first published book devoted to the theory of differential equations with non-instantaneous impulses. It aims to equip the reader with mathematical models and theory behind real life processes in physics, biology, population dynamics, ecology and pharmacokinetics. The authors examine a wide scope of differential equations with non-instantaneous impulses through three comprehensive chapters, providing an all-rounded and unique presentation on the topic, including:

- Ordinary differential equations with non-instantaneous impulses (scalar and n-dimensional case)
- Fractional differential equa
tions with non-instantaneous impulses (with Caputo fractional derivatives of order q ϵ (0, 1))
- Ordinary differential equations with non-instantaneous impulses occurring at random moments (with exponential, Erlang, or Gamma distribution)

Each chapter focuses on theory, proofs and examples, and contains numerous graphs to enrich the reader’s understanding. Additionally, a carefully selected bibliography is included. Graduate students at various levels as well as researchers in differential equations and related fields will find this a valuable resource of both introductory and advanced material.

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Schlagwörter

fractional differential equations, impulse systems, Lyapunov functions, non-instantaneous impulses in differential equations, ordinary differential equations, Caputo fractional derivatives, fractional derivatives, partial differential equations, differential equations, non-instantaneous impulses