- 學位論文
利用分數微積分求得某特定類微分方程的解
Solutions of Some Certain Classes of Differential Equations by Means of Fractional Calculus
並列摘要
During the past three decades or so, the widely-investigated subject of fractional calculus has remarkably gained importance and popularity due to its demonstrated applications in numerous diverse fields of science and engineering. It covers the widely known classical field, such as Abel's integral equation and viscoelasticity, also less well-known fields, including analysis of feedback amplifiers, capacitor theory, fractances, generalized voltage dividers, fractional-order Chua-Hartley systems, electrode-electrolyte interface models, fractional multipoles, electric conductance of biological systems, fractional-order models of neurons, fitting of experimental data, and the fields of special functions, ordinary and partial differential equations, integral equations, and summation of series, and others. Especially, it is used to solve various problems of the homogeneous and nonhomogeneous second order differential equations. The purpose of this thesis is using the fractional calculus approach to solve the Legendre and Bessel's differential equations which are merely solved by the traditional approach of power series solutions. We solve not only these two problems, but also the generalized forms of these differential equations.