A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel
In this paper, we introduce the Yang transform homotopy perturbation method (YTHPM), which is a novel method. We provide formulae for the Yang transform of Caputo-Fabrizio fractional order derivatives. We derive an algorithm for the solution of Caputo-Fabrizio (CF) fractional order partial different...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/8770488 |
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| _version_ | 1832546085413847040 |
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| author | Shabir Ahmad Aman Ullah Ali Akgül Manuel De la Sen |
| author_facet | Shabir Ahmad Aman Ullah Ali Akgül Manuel De la Sen |
| author_sort | Shabir Ahmad |
| collection | DOAJ |
| description | In this paper, we introduce the Yang transform homotopy perturbation method (YTHPM), which is a novel method. We provide formulae for the Yang transform of Caputo-Fabrizio fractional order derivatives. We derive an algorithm for the solution of Caputo-Fabrizio (CF) fractional order partial differential equation in series form and show its convergence to the exact solution. To demonstrate the novel approach, we include some examples with detailed solutions. We use tables and graphs to compare the exact and approximate solutions. |
| format | Article |
| id | doaj-art-c20e9283435f45b1a51af272e554b0d3 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-c20e9283435f45b1a51af272e554b0d32025-02-03T07:23:53ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/87704888770488A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay KernelShabir Ahmad0Aman Ullah1Ali Akgül2Manuel De la Sen3Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, PakistanSiirt University, Art and Science Faculty, Department of Mathematics, TR-56100 Siirt, TurkeyInstitute of Research and Development of Processes Faculty of Science and Technology University of the Basque Country Campus of Leioa (Bizkaia) 644-Leioa, SpainIn this paper, we introduce the Yang transform homotopy perturbation method (YTHPM), which is a novel method. We provide formulae for the Yang transform of Caputo-Fabrizio fractional order derivatives. We derive an algorithm for the solution of Caputo-Fabrizio (CF) fractional order partial differential equation in series form and show its convergence to the exact solution. To demonstrate the novel approach, we include some examples with detailed solutions. We use tables and graphs to compare the exact and approximate solutions.http://dx.doi.org/10.1155/2021/8770488 |
| spellingShingle | Shabir Ahmad Aman Ullah Ali Akgül Manuel De la Sen A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel Journal of Function Spaces |
| title | A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel |
| title_full | A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel |
| title_fullStr | A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel |
| title_full_unstemmed | A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel |
| title_short | A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel |
| title_sort | novel homotopy perturbation method with applications to nonlinear fractional order kdv and burger equation with exponential decay kernel |
| url | http://dx.doi.org/10.1155/2021/8770488 |
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