On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem
In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional deriv...
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| Format: | Article |
| Language: | English |
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MDPI AG
2015-02-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/17/2/885 |
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| author | Soheil Salahshour Ali Ahmadian Norazak Senu Dumitru Baleanu Praveen Agarwal |
| author_facet | Soheil Salahshour Ali Ahmadian Norazak Senu Dumitru Baleanu Praveen Agarwal |
| author_sort | Soheil Salahshour |
| collection | DOAJ |
| description | In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville) or a solution with increasing length of their support (Hukuhara difference). Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method. |
| first_indexed | 2024-04-13T06:26:07Z |
| format | Article |
| id | doaj.art-0e05e20f4dce4d73b46ef25db03033b1 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T06:26:07Z |
| publishDate | 2015-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0e05e20f4dce4d73b46ef25db03033b12022-12-22T02:58:26ZengMDPI AGEntropy1099-43002015-02-0117288590210.3390/e17020885e17020885On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset ProblemSoheil Salahshour0Ali Ahmadian1Norazak Senu2Dumitru Baleanu3Praveen Agarwal4Young Researchers and Elite Club, Mobarakeh Branch, Islamic Azad University, Mobarakeh, IranDepartment of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400UPM, Serdang, Selangor, MalaysiaDepartment of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400UPM, Serdang, Selangor, MalaysiaDepartment of Mathematics and Computer Sciences, Faculty of Art and Sciences, Cankaya University, Balgat 0630, Ankara, TurkeyDepartment of Mathematics, Anand International College of Engineering, Jaipur-303012, IndiaIn this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville) or a solution with increasing length of their support (Hukuhara difference). Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method.http://www.mdpi.com/1099-4300/17/2/885fuzzy fractional differential equationfuzzy Laplace transformCaputo differentiabilitydynamical systemsBasset problem |
| spellingShingle | Soheil Salahshour Ali Ahmadian Norazak Senu Dumitru Baleanu Praveen Agarwal On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem Entropy fuzzy fractional differential equation fuzzy Laplace transform Caputo differentiability dynamical systems Basset problem |
| title | On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem |
| title_full | On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem |
| title_fullStr | On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem |
| title_full_unstemmed | On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem |
| title_short | On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem |
| title_sort | on analytical solutions of the fractional differential equation with uncertainty application to the basset problem |
| topic | fuzzy fractional differential equation fuzzy Laplace transform Caputo differentiability dynamical systems Basset problem |
| url | http://www.mdpi.com/1099-4300/17/2/885 |
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