Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag–Leffler kernel differential operator
In this research study, fuzzy fractional differential equations in presence of the Atangana–Baleanu–Caputo differential operators are analytically and numerically treated using extended reproducing kernel Hilbert space technique. With the utilization of a fuzzy strongly generalized differentiability...
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| Published in | Mathematical methods in the applied sciences Vol. 46; no. 7; pp. 7965 - 7986 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Freiburg
Wiley Subscription Services, Inc
15.05.2023
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| Subjects | |
| Online Access | Get full text |
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| Abstract | In this research study, fuzzy fractional differential equations in presence of the Atangana–Baleanu–Caputo differential operators are analytically and numerically treated using extended reproducing kernel Hilbert space technique. With the utilization of a fuzzy strongly generalized differentiability form, a new fuzzy characterization theorem beside two fuzzy fractional solutions is constructed and computed. To besetment the attitude of fuzzy fractional numerical solutions, analysis of convergence and conduct of error beyond the reproducing kernel theory are explored and debated. In this tendency, three computational algorithms and modern trends in terms of analytic and numerical solutions are propagated. Meanwhile, the dynamical characteristics and mechanical features of these fuzzy fractional solutions are demonstrated and studied during two applications via three‐dimensional graphs and tabulated numerical values. In the end, highlights and future suggested research work are eluded. |
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| AbstractList | In this research study, fuzzy fractional differential equations in presence of the Atangana–Baleanu–Caputo differential operators are analytically and numerically treated using extended reproducing kernel Hilbert space technique. With the utilization of a fuzzy strongly generalized differentiability form, a new fuzzy characterization theorem beside two fuzzy fractional solutions is constructed and computed. To besetment the attitude of fuzzy fractional numerical solutions, analysis of convergence and conduct of error beyond the reproducing kernel theory are explored and debated. In this tendency, three computational algorithms and modern trends in terms of analytic and numerical solutions are propagated. Meanwhile, the dynamical characteristics and mechanical features of these fuzzy fractional solutions are demonstrated and studied during two applications via three‐dimensional graphs and tabulated numerical values. In the end, highlights and future suggested research work are eluded. |
| Author | Maayah, Banan Alhodaly, Mohammed Abu Arqub, Omar Singh, Jagdev |
| Author_xml | – sequence: 1 givenname: Omar orcidid: 0000-0001-9526-6095 surname: Abu Arqub fullname: Abu Arqub, Omar email: o.abuarqub@bau.edu.jo organization: Al‐Balqa Applied University – sequence: 2 givenname: Jagdev orcidid: 0000-0001-6853-4138 surname: Singh fullname: Singh, Jagdev organization: JECRC University – sequence: 3 givenname: Banan surname: Maayah fullname: Maayah, Banan organization: The University of Jordan – sequence: 4 givenname: Mohammed surname: Alhodaly fullname: Alhodaly, Mohammed organization: King Abdulaziz University |
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| SubjectTerms | Algorithms Boundary value problems characterization theorem Differential equations Fractional calculus fuzzy ABC FFIVP fuzzy ABC fractional derivative fuzzy ABC solution Hilbert space Kernels numerical analytical RKHSM Operators (mathematics) |
| Title | Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag–Leffler kernel differential operator |
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