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arXiv · 1510.00408

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

Ryan M. Evans·Udita N. Katugampola·David A. Edwards
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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 $\frac{1}{2}$ 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.

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Ryan M. Evans, Udita N. Katugampola, David A. Edwards. 2016-11-12. Applications of fractional calculus in solving Abel-type integral equations: Surface-volume reaction problem. https://arxiv.org/abs/1510.00408

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