Fractional Differential and Fractional Integro-Differential Equations: Qualitative Theory, Numerical Simulations, and Symmetry Analysis

Dear Colleagues,

In the last three decades, fractional calculus, fractional differential and fractional integro-differential equations, and qualitative theory of these equations have been broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the theory of fractional calculus, the qualitative theory of fractional differential and fractional integro-differential equations, their numerical simulations, and symmetry analysis are mathematical analysis tools applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. Fractional order operators are nonlinear operators that are more useful than classical formulations. Qualitative theory of fractional differential equations, fractional integro-differential equations, and fractional order operators can occur in numerous scientific fields, such as fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing, entropy theory, and so on. This is why the applications of theory of fractional calculus and qualitative theory of the mentioned equations have become a focus of international academic research, and a lot of researchers have adopted them in their new studies. One of the most recently developed studies is the use of different types of kernels. Singular and non-singular kernels have been used in recent studies for the analysis of dynamical models, and their results are comparable to those of classical work.

Prof. Dr. Cemil Tunç
Prof. Dr. Jen-Chih Yao
Prof. Dr. Mouffak Benchohra
Prof. Dr. Ahmed M. A. El-Sayed
Guest Editors

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