| Title |
Algebraic transformations for the analysis of fractional differential equations / |
| Translation of Title |
Algebrinės transformacijos trupmeninės eilės diferencialinių lygčių tyrimui. |
| Authors |
Telksnienė, Inga |
| Full Text |
|
| Pages |
128 |
| Keywords [eng] |
fractional differential equation ; operator calculus ; fractional power series ; algebraic transformations |
| Abstract [eng] |
Caputo fractional differential equations (CFDEs) have recently emerged as an important tool for modeling complex phenomena in a variety of scientific fields owing to their ability to model systems exhibiting memory or hereditary properties. The extensive applicability of Caputo's differential equations necessitates their exploration via both analytical and numerical techniques, making it a highly relevant task. Thus, the main objective of this thesis is to develop a novel semi-analytical framework for the construction and analysis of solutions to Caputo fractional differential equations by utilizing the concepts of Caputo algebra of fractional power series. This doctoral dissertation is based on a collection of the scientific papers. The first paper paved the way for this research by developing a novel methodology for the construction of fractional power series solutions to a specific Riccati-type CFDE. The presented results were expanded upon significantly in the second paper by demonstrating that a refined methodology can be utilized not only for the Riccati-type CFDEs, but for a wider range of equations including CFDEs with polynomial nonlinearity. The next step, published in the third paper, was concerned with using the developed methodology to create a semi-analytical scheme aimed towards the construction of approximate solutions to CFDEs. The final paper presented in this thesis brought all the previous research together to develop a comprehensive approach for the construction of solutions to an even wider class of nonlinear CFDEs. |
| Dissertation Institution |
Kauno technologijos universitetas. |
| Type |
Doctoral thesis |
| Language |
English |
| Publication date |
2024 |
