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

Abstract In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling surface–volume reactions in optical biosensors. We solve these equations by employing techniques from fractional calculus; several examples are discussed. Furthermore, for the first time, we encounter an order of the fractional derivative other than 1 2 in an applied problem. Hence, in this paper we explore the applicability of fractional calculus in real-world applications, further strengthening the true nature of fractional calculus.