Symmetry in Fractional Calculus: Advances and Applications

Dear Colleagues,

The subject convex analysis is very important in the theoretical aspects of mathematics and also for economists and physicists. Mathematicians use this theory, to provide the solution to problems that arise in mathematics. This theory touches almost all branches of mathematics.

Convex functions play an important role in many areas of mathematics, as well as in other areas of science economy, engineering, medicine, industry, and business. It is especially important in the study of optimization problems, where it is distinguished by several convenient properties (for example, any minimum of a convex function is a global minimum, or the maximum is attained at a boundary point). This explains why there is a very rich theory of convex functions and convex sets. Optimization of convex functions has many practical applications (circuit design, controller design, modeling, etc.). Due to a lot of importance, the term ‘convexity’ has become a rich source of inspiration and absorbing field for researchers.

Fractional calculus manages the investigation of supposed fractional derivatives and integrations over complex areas and their applications. Fractional calculus is the purported assignment of differentiations and integrations of arbitrary non-integer order. Lately, it has kept the consideration of several mathematicians because of its real-life applications. More importantly, it has turned into a valuable tool for handling the elements of perplexing frameworks from different parts of pure and applied sciences. On the other hand, the concept of symmetry is a beauty structure used to describe the environment and problems of the real world, as well as to strengthen the relationship between mathematical science and applied science such as physics and engineering. Therefore, the concept of symmetry exists in fractional calculus as in many other fields.

The purpose of this Special Issue is to pay tribute to the significant contributions and recent advances in theories, methods, and applications, including, but not limited to, the following Symmetry related fields:

• Convex functions;
• Symmetry in fractional models and operators;
• Fractional integral inequality;
• Generalized functions (distributions);
• Special functions and Mittag–Leffler function;
• Integral transforms;
• Optimization and optimal control theory;
• Game theory and dynamical systems;
• Hermite–Hadamard, Ostrowski, Simpson, Jensen–Mercer type inequalities, etc.;
• Quantum, post-quantum calculus;
• Symmetry on fractal and fractional differential operators.

Dr. Hijaz Ahmad
Prof. Dr. Predrag S. Stanimirović
Guest Editors

Manuscript Submission Information

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• convex functions
• symmetry in fractional models and operators
• fractional integral inequality
• generalized functions (distributions)
• special functions and Mittag–Leffler function
• integral transforms
• optimization and optimal control theory
• game theory and dynamical systems
• Hermite–Hadamard, Ostrowski, Simpson, Jensen–Mercer type inequalities, etc.
• quantum, post-quantum calculus
• symmetry on fractal and fractional differential operators