Laplace transforms of fractional calculus and some of the biophysical applications

In this study, Laplace transforms for fractional calculus and some of the biophysical applications are investigated. The thesis consists of four chapters. The first chapter is the introduction. The second chapter consists of mathematical background. This chapter involves Laplace transforms, the Gamma function, the Error function, the Dawson function, the Mittag-Leffler function and graphics of these functions. The third section is related to the mathematical tools of fractional calculus. This chapter consists of fractional integration, Riemann-Liouville fractional integration, Weyl fractional integration, fractional derivatives, fractional integration and derivation relations for the Laplace transform, and the topics of fractional order differential equations. The fourth chapter consists of a fractional analysis, some of the biophysical applications. In this chapter, the fractional derivatives and fractional order differential equations can be identified with a biophysical model of the problem as an example of simple nerve stimulation were examined.