Non-Instantaneous Impulses in Differential Equations

1. Front Matter

   Pages i-xi

   PDF

2. Non-instantaneous Impulses in Differential Equations

   • Ravi Agarwal, Snezhana Hristova, Donal O’Regan

   Pages 1-72

3. Non-instantaneous Impulses in Differential Equations with Caputo Fractional Derivatives

   • Ravi Agarwal, Snezhana Hristova, Donal O’Regan

   Pages 73-192

4. Non-instantaneous Impulses on Random Time in Differential Equations with Ordinary/Fractional Derivatives

   • Ravi Agarwal, Snezhana Hristova, Donal O’Regan

   Pages 193-244

5. Back Matter

   Pages 245-251

   PDF

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.

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

“The presence of a huge amount of illustrative examples and graphs anywhere in the book is very helpful for understanding of the theory and proofs. Graduate students at various levels as well as researchers in differential equations and related fields will find this book a valuable resource of both introductory and advanced material.” (Hristo S. Kiskinov, zbMATH 1426.34001, 2020)

• Department of Mathematics, Texas A&M University—Kingsville, Kingsville, USA

  Ravi Agarwal

• Department of Applied Mathematics, Plovdiv University, Plovdiv, Bulgaria

  Snezhana Hristova

• School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

  Donal O'Regan

Ravi P. Agarwal is a professor and the chair in the Department of Mathematics at Texas A&M University, Kingsville.

Snezhana Hristova is a professor in the Department of Applied Mathematics and Modeling at Plovdiv University in Plovdiv, Bulgaria.

Donal O'Regan is a professor in the School of Mathematics, Statistics and Applied Mathematics at the National University of Ireland in Galway, Ireland.

Policies and ethics