Bioconvection is the phenomenon of macroscopic convection motion of a fluid generated by the density gradient, caused by the directional collective swimming of microorganisms. These motile microorganisms can be classified according to the cause to which the movement of the microorganism is a response, such as gyrotactic, oxytactic, gravitactic, or chemotactic. These self-propelled motile microorganisms accumulate near the upper portion of the fluid layer, which builds up a dense upper surface and becomes unstable or destabilized. The upward swimming then causes a crumbling of microorganisms and the development of macroscopic convection. Bioconvection can be found in a wide range of applications, such as the pharmaceutical industry, biological polymer synthesis, environmentally-friendly applications, sustainable fuel cell technologies, microbial enhanced oil recovery, biosensors and biotechnology, and continuous refinements in mathematical modeling.

Recently, mathematical modeling of nanofluids as a novel class of heat transfer fluids that play a vital role in many industries has been widely considered by researchers. Due to the variety of applications, there are many steady problems in fluid dynamics, especially in the heat transfer flow of nanofluids and hybrid nanofluids, respectively. Unsteady bioconvection has still not been addressed in the existing literature with innovative fractional derivatives. Furthermore, there is still a space to discuss their fractional models theoretically and experimentally, which are open problems in applied mathematics. Usually, these models are represented in terms of traditional integer-order partial differential equations (PDEs). However, traditional PDEs cannot decode the complex behavior of physical flow parameters and memory effects. To combat these defects, research has focused on fractional dynamic systems of heat transfer in nanofluids. There also exist challenges in the applicability of fractional order systems with singular/non-singular and local/non-local kernels.

In this Special Issue, we aim to combine fractional models of heat transfer in nanofluids in the presence of unsteady bio convection in terms of both theory and applications. We welcome both original research and review articles.

Potential topics include but are not limited to the following:

• Heat transfer in fractional nanofluids with unsteady bioconvection
• Heat transfer in fractional hybrid nanofluids with unsteady bioconvection
• Heat transfer in bioconvection models with singular/non-singular and local/nonlocal kernels
• Biological applications and bio-microsystems with fractional derivatives
• Numerical and analytical solutions for heat transfer of fractional bioconvection problems for different surfaces
• Mathematical models of fractional hybrid nanofluids
• Fractional bio nanofluids with unsteady bioconvection