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

Autor:	Evans, Ryan M., Katugampola, Udita N., Edwards, David A.
Rok vydání:	2015
Předmět:	Mathematics - Classical Analysis and ODEs 26A33 92C45
Druh dokumentu:	Working Paper
Popis:	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. Comment: 19 pages, 2 figures, Preprint submitted for publication
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1510.00408 Zobrazit plný text záznamu View this record from Arxiv