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Full Description
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 equations 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.
Contents
Preface.- Introduction.- 1. Non-instantaneous Impulses in Differential Equations.- 2. Non-instantaneous Impulses in Differential Equations with Caputo fractional derivatives.- 3. Non-instantaneous Impulses on Random time in Differential Equations with Ordinary/Fractional Derivatives.- Bibliography.
