RIEMANN -LIOUVILLE FRACTIONAL DIFFERENT EQUATIONS
This final project discusses Riemann-Liouville Fractional Differential Equations from the existence and uniqueness of solutions to the methods of solving these type of differential equations. We begin from the definition of fractional calculus of both integral and derivative by generalizing integer...
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| 格式: | Final Project |
| 語言: | Indonesia |
| 在線閱讀: | https://digilib.itb.ac.id/gdl/view/22008 |
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| 機構: | Institut Teknologi Bandung |
| 語言: | Indonesia |
| 總結: | This final project discusses Riemann-Liouville Fractional Differential Equations from the existence and uniqueness of solutions to the methods of solving these type of differential equations. We begin from the definition of fractional calculus of both integral and derivative by generalizing integer order to arbitrary real numbers. Then, we continue to explain in detail the methods to solve linear fractional differential equations with constant coefficients by using Volterra Integral of the second kind and Laplace Transform. Furthermore, we use Mellin Transform to solve linear fractional differential equations with polynomial coefficients in the form of xα for α > 0. The important result from this final project shows that the fundamental solutions of linear fractional differential equations with constant coeficients can be expressed in Mittag-Leffler function which is a generalization of exponential function whereas the fundamental solutions of linear fractional differential equations with polynomial coeficients can be written as convolution analogue to Green Function. |
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