Manuscript Topics

In interdisciplinary approaches, which necessarily combine concepts and tools from different fields, mathematics is commonly the language used to smartly merge all the different concepts into a unique model. Cross-border modeling and numerical simulation work within the subfields of Physics and Engineering are particularly welcome in this special issue.

This Special Issue, “Recent advances in differential and partial differential equations and its applications”, will be destined for the publication of high-quality mathematical papers in the area of functional differential equations. Emphasis is placed on developments in the theory of delay differential, integrodifferential, impulsive differential, and ODE/PDE and their applications. Among possible topics of the papers, we can note, for example, the following: Various boundary value problems, the positivity/negativity of their solutions, Green’s functions and their properties, existence, and uniqueness solutions of nonlinear boundary value problems, optimization, and control theory, stability theory, oscillation and non-oscillation, variational problems, the use of functional differential equations in technology, economics, biology, and medicine.

The scope includes (but is not limited to) original research works providing characterizations, explanations, predictions of systems, and phenomena supporting the emergence of potentially novel, useful applications which can even be at a very early stage of conception. Papers based on the advances in the theory of stochastic processes and stochastic models of ODE/PDE are also welcome. The papers devoted to local and nonlocal conditions and transference differential equations of heat and mass transference mathematical processes in continuous media with memory and in media with fractal structure will be considered. These papers shall investigate modified initial and mixed boundary value problems for generalized transfer differential equations of integral and fractional orders. The fields of qualitative and quantitative analysis of nonlinear evolution equations and their applications in image analysis. Both analytical studies, as well as simulation-based studies, will be considered. We will cover Mathematical Problems in Materials Science, Mathematical Approaches to Image Processing with Applications, Applications of Partial Differential Equations, Recent Advances in Delay Differential and Difference Equations, Nonlinear Optimization, Variational Inequalities, and Equilibrium Problems, Computational Methods in Analysis and Applications, and all applied mathematical fields.

Some of topics on which papers can be focused are:  
• Functional differential equations  
• ODE and PDE with applications  
• Fractional PDE  
• Fractional numerical analysis  
• Oscillation/nonoscillation  
• Feedback control  
• Stability  
• Boundary value problems  
• Markov chains  
• Jump processes  
• Coupled dynamics  
• Fractional processes  
• Space-time fractional equations  
• Fractional Brownian motion  
• Long-range dependence  
• Boundary value problem  
• Fractional integral  
• Time-space fractional vibration equation  
• Convergence  
• Stability  
• Eigenvalue/eigenfunction  
• Green function

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