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On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type.
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Hernández-Hernández, Ma Elena (2016) On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type. PhD thesis, University of Warwick.
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WRAP_Theses_Hernandez-Hernandez_2016.pdf - Submitted Version - Requires a PDF viewer. Download (1298Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3065933~S15
Abstract
This dissertation focuses on the study of generalized fractional differential equations involving a general class of non-local operators which are referred to as the generalized fractional derivatives of Caputo and Riemann-Liouville (RL) type. These operators were introduced recently as a probabilistic extension of the classical fractional Caputo and Riemann-Liouville derivatives of order β ε (0,1) (when acting on regular enough functions).
The main contribution of this work lies in displaying the use of stochastic analysis as a valuable approach for the study of fractional differential equations and their generalizations. The stochastic representations presented here also lead to many interesting potential applications, e.g., by providing new numerical approaches to approximate solutions to equations for which an explicit solution is not available.
| Item Type: | Thesis or Dissertation (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Fractional differential equations, Fractional calculus | ||||
| Official Date: | October 2016 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Department of Statistics | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Kolokolʹt︠s︡ov, V. N. (Vasiliĭ Nikitich) | ||||
| Sponsors: | University of Warwick. Department of Statistics ; University of Warwick. Chancellor International Scholarship ; Mexico. Secretaría de Educación Pública. Dirección General de Relaciones Internacionales | ||||
| Format of File: | |||||
| Extent: | xi, 164 leaves : illustrations | ||||
| Language: | eng |
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