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Functional equations and dynamical systems on time scales are two interconnected areas of mathematics that provide a framework for studying the behavior of functions and systems over both continuous and discrete time domains. In particular,

Functional equations are equations that involve functions as variables. They often arise in various fields, including mathematics, physics, engineering, and economics, as a means to model relationships between variables that are not directly related by ordinary algebraic equations. Functional equations can be classified into different types, such as linear, nonlinear, differential, integral, and more. They have applications in various areas, including the stability of solutions, optimization problems, and modeling complex systems.

On the other hand, Dynamical systems on time scales provide a unified framework for studying both continuous and discrete time systems. Time scales theory generalizes the concepts of real numbers and integers to a more general mathematical structure that encompasses both continuous and discrete time. Time scales allow mathematicians and researchers to bridge the gap between continuous and discrete dynamics, making it easier to analyze systems that exhibit mixed behaviors.

The study of functional equations and dynamical systems on time scales has several key objectives and applications, including:
•  Analyzing and understanding the behavior of systems that combine continuous and discrete dynamics, which can occur in various real-world situations.
•  Investigating the stability and existence of solutions to various types of functional equations on time scales.
•  Developing methods for solving complex systems of differential or difference equations, which may have applications in physics, engineering, and biology.
•  Studying the periodicity and long-term behavior of systems with both continuous and discrete components.

This special issue complements the aim of the journal since functional equations and dynamical systems occupy huge areas in mathematics and have abundant applications.

The major aim of this special issue is for authors from scientific disciplines to publish high quality research on recent developments in the field of dynamical systems and related applications. Topics for this special issue may include, but are not limited to, the following:

•  Qualitative theory of differential equations including partial differential equations
•  Boundary value problems
•  Integral equations
•  Integro-differential equations

A special issue focused on dynamical systems and related applications in scientific disciplines can cover a wide range of topics. Here are some key areas and topics that you might consider including in such a special issue:
    1. Nonlinear Dynamics and Chaos Theory:
        •  Bifurcation theory
        •  Strange attractors
        •  Fractals in dynamical systems
    2. Applications in Physics:
        •  Celestial mechanics
        •  Fluid dynamics
        •  Quantum mechanics
        •  Classical mechanics
    3. Applications in Engineering:
        •  Control theory
        •  Robotics
        •  Vibrations and structural dynamics
        •  Electrical circuits and systems
    4. Applications in Biology:
        •  Population dynamics
        •  Epidemiology modeling
        •  Neurodynamics
        •  Evolutionary dynamics

Keywords: Functional Equations, Dynamical systems, Integral equations, Integro-differential equations, Time scales

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