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

作者：Evans Ryan M; Katugampola Udita N; Edwards David A

来源：COMPUTERS %26 MATHEMATICS WITH APPLICATIONS, 2017, 73(6): 1346-1362.

DOI：10.1016/j.camwa.2016.12.005

• Abel integral equation
• Riemann-Liouville integral
• Caputo fractional derivative
• Fractional calculus
• Surface-volume reactions

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.

• 出版日期2017-3-15