Stability Analysis and Computational Interpretation of an Effective Semi Analytical Scheme for Fractional Order Non-Linear Partial Differential Equations
In this study we will check the stability of the semi analytical technique, the Laplace variational iteration (LVI) scheme, which is the combination of a variational iteration technique and the Laplace transform method. Then, we will apply it to solve some non-linear fractional order partial differe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/7/393 |
| _version_ | 1797406324638613504 |
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| author | Javed Iqbal Khurram Shabbir Liliana Guran |
| author_facet | Javed Iqbal Khurram Shabbir Liliana Guran |
| author_sort | Javed Iqbal |
| collection | DOAJ |
| description | In this study we will check the stability of the semi analytical technique, the Laplace variational iteration (LVI) scheme, which is the combination of a variational iteration technique and the Laplace transform method. Then, we will apply it to solve some non-linear fractional order partial differential equations. Since the Laplace transform cannot be applied to non-linear problems, the combination of the variational iteration technique with it will give a better and rapidly convergent sequence. Exact solutions may also exist, but we will show that the coupled technique is much better to approximate the exact solutions. The Caputo–Fabrizio fractional derivative will be used throughout the study. In addition, some possible implications of the results given here are connected with fixed point theory. |
| first_indexed | 2024-03-09T03:23:48Z |
| format | Article |
| id | doaj.art-bcb2759d57bc4d5b8075429a31b68736 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T03:23:48Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-bcb2759d57bc4d5b8075429a31b687362023-12-03T15:04:56ZengMDPI AGFractal and Fractional2504-31102022-07-016739310.3390/fractalfract6070393Stability Analysis and Computational Interpretation of an Effective Semi Analytical Scheme for Fractional Order Non-Linear Partial Differential EquationsJaved Iqbal0Khurram Shabbir1Liliana Guran2Department of Mathematics, Government College University, Lahore 54000, PakistanDepartment of Mathematics, Government College University, Lahore 54000, PakistanDepartment of Pharmaceutical Sciences, “Vasile Goldiş” Western University of Arad, L. Rebreanu Street, No. 86, 310048 Arad, RomaniaIn this study we will check the stability of the semi analytical technique, the Laplace variational iteration (LVI) scheme, which is the combination of a variational iteration technique and the Laplace transform method. Then, we will apply it to solve some non-linear fractional order partial differential equations. Since the Laplace transform cannot be applied to non-linear problems, the combination of the variational iteration technique with it will give a better and rapidly convergent sequence. Exact solutions may also exist, but we will show that the coupled technique is much better to approximate the exact solutions. The Caputo–Fabrizio fractional derivative will be used throughout the study. In addition, some possible implications of the results given here are connected with fixed point theory.https://www.mdpi.com/2504-3110/6/7/393Laplace transformvariational iteration methodnonlinear partial differential equationsfractional derivative operatorsespecially Caputo–Fabrizio fractional derivative operatorfixed point |
| spellingShingle | Javed Iqbal Khurram Shabbir Liliana Guran Stability Analysis and Computational Interpretation of an Effective Semi Analytical Scheme for Fractional Order Non-Linear Partial Differential Equations Fractal and Fractional Laplace transform variational iteration method nonlinear partial differential equations fractional derivative operators especially Caputo–Fabrizio fractional derivative operator fixed point |
| title | Stability Analysis and Computational Interpretation of an Effective Semi Analytical Scheme for Fractional Order Non-Linear Partial Differential Equations |
| title_full | Stability Analysis and Computational Interpretation of an Effective Semi Analytical Scheme for Fractional Order Non-Linear Partial Differential Equations |
| title_fullStr | Stability Analysis and Computational Interpretation of an Effective Semi Analytical Scheme for Fractional Order Non-Linear Partial Differential Equations |
| title_full_unstemmed | Stability Analysis and Computational Interpretation of an Effective Semi Analytical Scheme for Fractional Order Non-Linear Partial Differential Equations |
| title_short | Stability Analysis and Computational Interpretation of an Effective Semi Analytical Scheme for Fractional Order Non-Linear Partial Differential Equations |
| title_sort | stability analysis and computational interpretation of an effective semi analytical scheme for fractional order non linear partial differential equations |
| topic | Laplace transform variational iteration method nonlinear partial differential equations fractional derivative operators especially Caputo–Fabrizio fractional derivative operator fixed point |
| url | https://www.mdpi.com/2504-3110/6/7/393 |
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