Qualitative Analysis of Fractional Deterministic and Stochastic Systems

Dear Colleagues,

Over the years, many results have emerged on the theory and applications of stochastic differential equations. In particular, fractional stochastic differential equations, which are a generalization of differential equations by the use of fractional and stochastic calculus, are more popular due to their applications in mathematical finance, biology, biomedicine, and so on. The research area of stochastic differential equations has occupied one of the primary areas of numerical and applied mathematics for the last three decades, providing new techniques for analyzing complex systems. Thus, it is of great importance to design stochastic effects in the study of fractional-order dynamical systems.

This Special Issue invites original contributions that cover recent advances in the theory and applications of fractional deterministic and stochastic differential equations. The main focus of this Special Issue is to describe and analyze new methods and techniques for solving nonlinear dynamical systems described by fractional deterministic and stochastic differential equations that examine important applications. We kindly invite strong and interesting contributions that provide original results obtained from modern computational techniques of theoretical, experimental, and applied aspects of both deterministic and stochastic fractional dynamic systems. We also strongly encourage young researchers/PhD students who have achieved exciting results under the supervision and guidance of their scientific advisors to submit their works to this Special Issue.

Potential topics include, but are not limited to:

• Stochastic fractional differential equations;
• Stochastic differential and partial differential equations (SPDEs);
• A class of backward stochastic differential equations with a conformable derivative;
• Stochastic differential equations with fractional Brownian motion;
• Mean-field stochastic equations;
• Instantaneous and non-instantaneous impulsive deterministic and fractional differential equations;
• Fractional reaction–diffusion and Navier–Stokes equation;
• Continuous and discrete fractional systems with randomness;
• Control and optimization for fractional deterministic and stochastic systems;
• Numerical methods for fractional-order stochastic systems;
• Stability analysis of fractional deterministic and stochastic systems;
• Optimal control;
• Fractional q-calculus;
• Fractional time-delay systems;
• Fractional Brownian process;
• Applications of fractional stochastic differential equations in finance and engineering;
• Stochastic analysis in finance;
• Stochastic analysis in biology and biomedicine.

Prof. Dr. Nazim Mahmudov
Prof. Dr. Rathinasamy Sakthivel
Prof. Dr. Carlo Cattani
Guest Editors

Manuscript Submission Information

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