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Description of inhomogeneous dielectric properties of a solvent in the vicinity of ions has been attracting research interests in mathematical modeling for many years. From many experimental results, it has been concluded that the dielectric response of a solvent linearly depends on the ionic strength within a certain range. Based on this assumption, a new implicit solvent model is proposed in the form of total free energy functional and a quasi-linear Poisson-Boltzmann equation (QPBE) is derived....
Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional...
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