Flow problems occur in most engineering industries. Many industrial flows possess are of nonlocal nature, so the modeling of flow problems with differential equations involves fractional derivatives. Governing flow equations for transport phenomena with fractional derivatives has been shown to be successful for analysis of flow characteristics. In recent times, modeling with fractional derivatives has received much attention in fluid mechanics and various other sciences. Impacts of modeling with fractional derivatives are seen in control theory, viscoelasticity, and electrochemistry. Various fractional derivatives have been studied in the literature to model flow problems. Artificial and natural mechanisms can be accurately understood by fractional derivatives because they describe the hereditary properties of substances.

Due to the freedom and nonlocal nature of fractional mathematical models, they have been studied by various researchers working in control theory, mathematics, and engineering. Fractional modeling has been successfully applied to various viscoelastic flow modeling, modeling of dynamical systems, control design of fractional problems, and parameter estimation. However, there are some unsolved nonlinear flow problems and there are challenges in fractional mathematical modeling of these flows, which deserve further investigation. New theories in fractional calculus will pave the way to model flow problems in a better way.

The main purpose of this Special Issue is to report the new developments in fractional mathematical modeling of flow problems. We welcome researchers to submit original research articles as well as review articles.

Potential topics include but are not limited to the following:

• Mathematical modeling of flow problems with fractional derivatives
• Modeling of heat and mass transfer with fractional derivatives
• Chemical processes in flow problems
• Optimization with a fractional differential approach
• Solution methodologies for fractional partial differential equations
• Modeling of convection and diffusion in flow problems
• Relaxation and retardation time phenomenon in flow problems
• Operator theory in fractional calculus
• Application of fractional calculus in mechanical engineering
• Modeling of processes in thermal engineering
• Numerical analysis and algorithms for fractional differential equations