Caputo-Fabrizio approach to numerical fractional derivatives
Fractional calculus is an essential tool in every area of science today. This work gives the quadratic interpolation-based L1-2 formula for the Caputo-Fabrizio derivative, a numerical technique for approximating the fractional derivative. To get quadratic and cubic convergence rates, respectively,...
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| Format: | Article |
| Language: | English |
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Department of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan University
2023-07-01
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| Series: | Bibechana |
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| Online Access: | https://www.nepjol.info/index.php/BIBECHANA/article/view/53971 |
| _version_ | 1797194066791759872 |
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| author | Shankar Pariyar Jeevan Kafle |
| author_facet | Shankar Pariyar Jeevan Kafle |
| author_sort | Shankar Pariyar |
| collection | DOAJ |
| description |
Fractional calculus is an essential tool in every area of science today. This work gives the quadratic interpolation-based L1-2 formula for the Caputo-Fabrizio derivative, a numerical technique for approximating the fractional derivative. To get quadratic and cubic convergence rates, respectively, we study the use of Lagrange interpolation in the L1 and L1-2 formulations. Our numerical analysis shows the accuracy of the theory’s predicted convergence rates. The L1-2 formula aims to enhance the accuracy and usability of a flexible tool for many applications in science and mathematics. We demonstrate the validity of the theory’s predicted convergence rates using numerical analysis. Several numerical examples are also given to show how the suggested approaches may be utilized to determine the Caputo-Fabrizio derivative of well-known functions. Lagrange interpolation is used in the L1 and L1-2 procedures to obtain quadratic and cubic convergence rates, respectively. The numerical study demonstrates that the L1-2 formula offers greater accuracy when compared to current approaches. In addition, it is a better apparatus for several applications in science and mathematics. Due to its higher convergence rate, the L1-2 formula outperforms other available numerical methods for scientific computations. The L1-2 formula, a novel numerical method for the Caputo-Fabrizio derivative that makes use of quadratic interpolation, is introduced in this study as a conclusion.
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| first_indexed | 2024-03-09T01:31:32Z |
| format | Article |
| id | doaj.art-a98f42021726415e8baae5aa496f2be4 |
| institution | Directory Open Access Journal |
| issn | 2091-0762 2382-5340 |
| language | English |
| last_indexed | 2024-04-24T05:50:23Z |
| publishDate | 2023-07-01 |
| publisher | Department of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan University |
| record_format | Article |
| series | Bibechana |
| spelling | doaj.art-a98f42021726415e8baae5aa496f2be42024-04-23T13:04:50ZengDepartment of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan UniversityBibechana2091-07622382-53402023-07-0120210.3126/bibechana.v20i2.5397181062Caputo-Fabrizio approach to numerical fractional derivativesShankar Pariyar0Jeevan Kafle1 Tri-Chandra Multiple Campus, Ghantaghar, Kathmandu and Centre Department of Mathematics, Kiritpur, Kathmandu, NepalCentral Department of Mathematics, Tribhuvan university, Kathmandu, Nepal Fractional calculus is an essential tool in every area of science today. This work gives the quadratic interpolation-based L1-2 formula for the Caputo-Fabrizio derivative, a numerical technique for approximating the fractional derivative. To get quadratic and cubic convergence rates, respectively, we study the use of Lagrange interpolation in the L1 and L1-2 formulations. Our numerical analysis shows the accuracy of the theory’s predicted convergence rates. The L1-2 formula aims to enhance the accuracy and usability of a flexible tool for many applications in science and mathematics. We demonstrate the validity of the theory’s predicted convergence rates using numerical analysis. Several numerical examples are also given to show how the suggested approaches may be utilized to determine the Caputo-Fabrizio derivative of well-known functions. Lagrange interpolation is used in the L1 and L1-2 procedures to obtain quadratic and cubic convergence rates, respectively. The numerical study demonstrates that the L1-2 formula offers greater accuracy when compared to current approaches. In addition, it is a better apparatus for several applications in science and mathematics. Due to its higher convergence rate, the L1-2 formula outperforms other available numerical methods for scientific computations. The L1-2 formula, a novel numerical method for the Caputo-Fabrizio derivative that makes use of quadratic interpolation, is introduced in this study as a conclusion. https://www.nepjol.info/index.php/BIBECHANA/article/view/53971Caputo fractional derivativesNumerical solutionAnalytical SolutionLagrange interpolationL1-2 formulaL1 formula |
| spellingShingle | Shankar Pariyar Jeevan Kafle Caputo-Fabrizio approach to numerical fractional derivatives Bibechana Caputo fractional derivatives Numerical solution Analytical Solution Lagrange interpolation L1-2 formula L1 formula |
| title | Caputo-Fabrizio approach to numerical fractional derivatives |
| title_full | Caputo-Fabrizio approach to numerical fractional derivatives |
| title_fullStr | Caputo-Fabrizio approach to numerical fractional derivatives |
| title_full_unstemmed | Caputo-Fabrizio approach to numerical fractional derivatives |
| title_short | Caputo-Fabrizio approach to numerical fractional derivatives |
| title_sort | caputo fabrizio approach to numerical fractional derivatives |
| topic | Caputo fractional derivatives Numerical solution Analytical Solution Lagrange interpolation L1-2 formula L1 formula |
| url | https://www.nepjol.info/index.php/BIBECHANA/article/view/53971 |
| work_keys_str_mv | AT shankarpariyar caputofabrizioapproachtonumericalfractionalderivatives AT jeevankafle caputofabrizioapproachtonumericalfractionalderivatives |