Qualitative Analysis of Differential Equations: Theory and Applications

Dear Colleagues,

In the past year, qualitative analyses, i.e., analyses of the stability, boundedness, integrability, existence and uniqueness  of solutions  of functional differential equations (delay differential equations, neutral differential equations, advanced differential equations and  impulsive differential equations); dynamic models; integral equations; integro-differential equations; partial  differential equations; fractional differential equations; fractional integro-differential equations; fractional partial  differential equations; etc., have attracted the attention of numerous researchers at the theoretical level and at the level of their applications. From the relevant literature, it can be observed that numerous processes and problems in biology, the interactions between species, population dynamics, microbiology, distributed networks, mechanics, medicine, nuclear reactors, chemistry, distributed networks, epidemiology, physics, engineering, economics, physiology, viscoelasticity, etc. can be modelled mathematically by these kind of equations.

Therefore, these kind of equations have vital, important roles in real world applications. However, these kind of equations can be solved analytically in particular cases, but not numerically. Qualitative theory can enable us to obtain information about the behaviour of solutions without prior information on them by means of Lyapunov’s second method, the fixed-point method, the Lyapunov–Krasovskii method, and so on. The aim of this SI is to collect some new theoretical contributions and real-world applications with regard to the qualitative theory of  the equations mentioned above. 

Dr. Osman Tunç
Prof. Dr. Vitalii Slynko
Prof. Dr. Sandra Pinelas
Guest Editors

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