Numerical methods for fractional differential equations by new caputo and hadamard types operators
Fractional ordinary differential equation (FODE) and fractional partial differential equation (FPDE) emerges in various modelling of physics phenomena. Over past decades, several fractional derivative and operator has been introduced such as Caputo-Fabrizio operator, Caputo-Hadamard fractional...
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| Format: | Thesis |
| Language: | English English English |
| Published: |
2020
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| Subjects: | |
| Online Access: | http://eprints.uthm.edu.my/957/1/24p%20TOH%20YOKE%20TENG.pdf http://eprints.uthm.edu.my/957/2/TOH%20YOKE%20TENG%20COPYRIGHT%20DECLARATION.pdf http://eprints.uthm.edu.my/957/3/TOH%20YOKE%20TENG%20WATERMARK.pdf |
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| Summary: | Fractional ordinary differential equation (FODE) and fractional partial differential
equation (FPDE) emerges in various modelling of physics phenomena. Over past
decades, several fractional derivative and operator has been introduced such as
Caputo-Fabrizio operator, Caputo-Hadamard fractional derivative, Marchaud
fractional derivative or Caputo fractional derivative. The fractional differential
equations defined in these fractional derivatives and operators definition are difficult
or impossible to solve analytically. Therefore, we seek after highly accurate
numerical scheme in efficient ways such as predictor-corrector method, finite
difference scheme and spectral collocation method in this research for FODE and
FPDE. Caputo-Fabrizo operator is a definition which is verified that does not fit the
usual concept neither for fractional nor for integer derivative integral. The main
interest of this operator is having regular kernel and which is a necessity of using a
model describing the behavior of classical viscoelastic materials, electromagnetic
system and viscoelastic materials. Furthermore, associated integral for Caputo�Fabrizio operator is also presented using Laplace transform and Inverse Laplace
transform. Hence, we first introduce predictor-corrector scheme involving Caputo�Fabrizo operator, α > 0 which represents higher order of approximation |
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