Studies in Evolution Equations and Related Topics

1. Front Matter

   Pages i-xiv

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2. Evolution Equations: Present and Future

   • Gaston M. N’Guérékata, Bourama Toni

   Pages 1-6

3. Invariant Stable Manifolds of \(\mathcal {E}\)-Class for Partial Neutral Functional Differential Equations on a Half-Line

   • Thi Ngoc Ha Vu, Thieu Huy Nguyen, Xuan Yen Trinh

   Pages 7-32

4. Global Attractor in Alpha-Norm for Some Partial Functional Differential Equations of Neutral and Retarded Type

   • Mostafa Adimy, Khalil Ezzinbi, Catherine Marquet

   Pages 33-49

5. A Study of an Epidemic SIR Model via Homotopy Analysis Method in the Sense of Caputo-Fractional System

   • Brice M. Yambiyo, Fatemeh Norouzi, Gaston M. N’Guérékata

   Pages 51-67

6. Structural Stability of Nonlinear Elliptic p(u)-Laplacian Problem with Robin Type Boundary Condition

   • Stanislas Ouaro, Noufou Sawadogo

   Pages 69-111

7. Optimal Control of Averaged State of a Population Dynamics Model

   • Cyrille Kenne, Boniface Nkemzi

   Pages 113-127

8. C ₀-Semigroup and Stepanov-Like Almost Automorphic Functions in Matched Spaces of Time Scales

   • Chao Wang, Gaston M. N’Guérékata

   Pages 129-154

9. A Reaction–Diffusion Model for Salmonella Transmission Within an Industrial Hens House with Distributed Resistance to Salmonella Carrier State

   • Pascal Zongo, Catherine Beaumont

   Pages 155-185

10. Impulsive Implicit Caputo Fractional q-Difference Equations in Finite- and Infinite-Dimensional Banach Spaces

    • Badr Alqahtani, Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata

    Pages 187-209

11. Null Controllability of a Degenerate Cascade Model in Population Dynamics

    • Younes Echarroudi, Lahcen Maniar

    Pages 211-268

This volume features recent development and techniques in evolution equations by renown experts in the field. Each contribution emphasizes the relevance and depth of this important area of mathematics and its expanding reach into the physical, biological, social, and computational sciences as well as into engineering and technology.


The reader will find an accessible summary of a wide range of active research topics, along with exciting new results. Topics include: Impulsive implicit Caputo fractional q-difference equations in finite and infinite dimensional Banach spaces; optimal control of averaged state of a population dynamic model; structural stability of nonlinear elliptic p(u)-Laplacian problem with Robin-type boundary condition; exponential dichotomy and partial neutral functional differential equations, stable and center-stable manifolds of admissible class; global attractor in Alpha-norm for some partial functional differential equations of neutral and retarded type; and more.


Researchers in mathematical sciences, biosciences, computational sciences and related fields, will benefit from the rich and useful resources provided. Upper undergraduate and graduate students may be inspired to contribute to this active and stimulating field.

• evolution equations
• fractional q-difference equations
• Caputo fractional derivative
• population dynamics
• optimal control
• structural stability
• Robin-type boundary condition
• exponential dichotomy
• neutral functional differential equations
• global attractor in Alpha-norm

• Department of Mathematics, Morgan State University, Baltimore, USA

  Gaston M. N'Guérékata

• Department of Mathematics, Howard University, Washington, DC, USA

  Bourama Toni

Gaston M. N'Guérékata is a University Distinguished Professor and Associate Dean of the School of Computer, Mathematical, and Natural Sciences at Morgan State University in Baltimore, Maryland, USA. He authored over 240 publications including 10 books at the graduate/research level. His research interests include almost periodic and almost automorphic functions, abstract harmonic analysis, fractional differential equations and spectral theory of bounded functions. Dr. N'Guérékata has been a keynote speaker at several international conferences and is the recipient of several research awards in the USA and abroad.


Bourama Toni is a Full Professor of Mathematics and Chair of the Department of Mathematics at Howard University, Washington, DC, USA. He is a Founder and Editor of the Springer-published STEAM-H series, with truly an interdisciplinary profile. Dr. Toni's research interests are primarily in Differential and Nonlinear Analysis and related topics to include Dynamical Systems, Non-Archimedean Analysis, Game Theory, Feedback Loops Analysis, and their applications to biosciences, behavioral sciences and naval engineering, with an excellent track-record of quality published research papers including contributed volumes with Springer.

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