Applications of fractional calculus in solving Abel-type integral equations: Surface-volume reaction problem

摘要

In this paper we consider a class of partial integro-differential equationsof fractional order, motivated by an equation which arises as a result ofmodeling surface-volume reactions in optical biosensors. We solve theseequations by employing techniques from fractional calculus; several examplesare discussed. Furthermore, for the first time, we encounter an order of thefractional derivative other than $\frac{1}{2}$ in an applied problem. Hence, inthis paper we explore the applicability of fractional calculus in real-worldapplications, further strengthening the true nature of fractional calculus.