Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions
The aim of this article is to propose a new definition of fuzzy fractional derivative, so-called fuzzy conformable. To this end, we discussed fuzzy conformable fractional integral softly. Meanwhile, uniqueness, existence, and other properties of solutions of certain fuzzy conformable fractional diff...
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| Published in | Soft computing (Berlin, Germany) Vol. 24; no. 16; pp. 12501 - 12522 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.08.2020
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1432-7643 1433-7479 |
| DOI | 10.1007/s00500-020-04687-0 |
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| Abstract | The aim of this article is to propose a new definition of fuzzy fractional derivative, so-called fuzzy conformable. To this end, we discussed fuzzy conformable fractional integral softly. Meanwhile, uniqueness, existence, and other properties of solutions of certain fuzzy conformable fractional differential equations under strongly generalized differentiability are also utilized. Furthermore, all needed requirements for characterizing solutions by equivalent systems of crisp conformable fractional differential equations are debated. In this orientation, modern trend and new computational algorithm in terms of analytic and approximate conformable solutions are proposed. Finally, the reproducing kernel Hilbert space method in the conformable emotion is constructed side by side with numerical results, tabulated data, and graphical representations. |
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| AbstractList | The aim of this article is to propose a new definition of fuzzy fractional derivative, so-called fuzzy conformable. To this end, we discussed fuzzy conformable fractional integral softly. Meanwhile, uniqueness, existence, and other properties of solutions of certain fuzzy conformable fractional differential equations under strongly generalized differentiability are also utilized. Furthermore, all needed requirements for characterizing solutions by equivalent systems of crisp conformable fractional differential equations are debated. In this orientation, modern trend and new computational algorithm in terms of analytic and approximate conformable solutions are proposed. Finally, the reproducing kernel Hilbert space method in the conformable emotion is constructed side by side with numerical results, tabulated data, and graphical representations. |
| Author | Arqub, Omar Abu Al-Smadi, Mohammed |
| Author_xml | – sequence: 1 givenname: Omar Abu orcidid: 0000-0001-9526-6095 surname: Arqub fullname: Arqub, Omar Abu email: o.abuarqub@ju.edu.jo organization: Department of Mathematics, Faculty of Science, The University of Jordan – sequence: 2 givenname: Mohammed surname: Al-Smadi fullname: Al-Smadi, Mohammed organization: Department of Applied Science, Ajloun College, Al-Balqa Applied University |
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| Keywords | Characterization theorem Fuzzy conformable fractional differential equation Fuzzy conformable derivative and integral Reproducing kernel Hilbert space method |
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| Snippet | The aim of this article is to propose a new definition of fuzzy fractional derivative, so-called fuzzy conformable. To this end, we discussed fuzzy conformable... |
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| SubjectTerms | Algorithms Artificial Intelligence Calculus Computational Intelligence Control Differential equations Engineering Fractional calculus Fuzzy sets Graphical representations Hilbert space Mathematical Logic and Foundations Mechatronics Methodologies and Application Robotics |
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| Title | Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions |
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