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

2015/09/26 by Ryan M. Evans, Evans, Ryan M., Udita N. Katugampola +3
Mathematics · #26A33 #92C45 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:26A33 #msc:92C45

paper · pdf · doi:10.48550/arxiv.1510.00408

19 pages, 2 figures, Preprint submitted for publication

arxiv created 2016/11/12 · arxiv updated 2016/11/15

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.

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