Mathematical and Computational Approaches to Fractal and Fractional Systems Using Fixed Point Theory

Dear Colleagues,

Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, selection and matching problems, and problems of proving the existence of solutions of integral and differential equations, image machine learning, signal recovery, pattern recognition, and so on. These challenging problems are increasingly difficult to construct, compute, and verify. Therefore, there has been a lot of interest in studying these problems because of their numerous applications. The development of systematic methods, which are efficient and reliable designs of the hybrid system, is highly demanded and the key to analyzing nonlinear systems. Fixed theory is a very strong mathematical tool to establish the existence and uniqueness of almost all problems by nonlinear relations. In addition, the stability criteria raise important questions about whether their various properties are stable; an unstable system is typically useless and potentially dangerous.

The Banach fixed point theorem states that each contraction in an iterated function system converges to a unique fixed point that is the fractal itself. By applying these contractions iteratively, the system is driven toward its fixed point attractor, allowing for the computational generation of complex fractal structures. Fractals can be thought of as the unique attractors of operators on the space of compact sets with the Hausdorff metric.

The objective of this Special Issue is to report the latest advancements in the solutions of real-world problems by using the fixed point and fractal theories. The solvability of such problems is usually investigated in specific function spaces. The choice of the appropriate fixed/best proximity point theorems and the use of the specific properties of the function spaces can have a big impact on the solvability of nonlinear equations. Special attention will be paid to various applications of fixed point theory to fractal analysis and fractional calculus, the branch of mathematics working with differentiation and integration of arbitrary real or complex order. Fractional calculus, especially the theory of fractional differential equations and fractional integral equations, has many applications in several scientific fields, for example, in mechanics, physics, chemistry, economics, biology, engineering, and so on.

Potential topics include, but are not limited to, the following:

• Fixed point theory;
• Fractal theory;
• Best proximity point theory;
• Topological fixed point theory;
• Fuzzy fixed/best proximity point theory;
• Image processing by fixed point theory;
• Decision making by fixed point theory;
• Stability analysis by fixed point theory;
• Existence of solutions of integral/differential/fractional/fractal fractional equations by fixed point theory;
• Optimization of fixed point theory;
• Existence of solution of mathematical models based on fixed point theory.

Prof. Dr. Ljubiša D. R. Kočinac
Dr. Tayyab Kamran
Guest Editors

Manuscript Submission Information

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• fixed points
• contraction mappings
• fractal analysis
• integral equations
• fractional differential equations
• optimization
• topological spaces
• decision making
• best proximity points
• stability analysis
• image processing
• fuzzy metric spaces
• mathematical modeling