A Nonlinear Implicit Fractional Equation with Caputo Derivative
In this paper, we study a nonlinear implicit differential equation with initial conditions. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of Banach principle. Then, another res...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5547003 |
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| author | Ameth Ndiaye |
| author_facet | Ameth Ndiaye |
| author_sort | Ameth Ndiaye |
| collection | DOAJ |
| description | In this paper, we study a nonlinear implicit differential equation with initial conditions. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of Banach principle. Then, another result that deals with the existence of at least one solution is delivered and some sufficient conditions for this result are established by means of the fixed point theorem of Schaefer. At the end, we discuss two examples to illustrate the applicability of the main results. |
| format | Article |
| id | doaj-art-62662bc652a44a94bb9e67058a984d6d |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-62662bc652a44a94bb9e67058a984d6d2025-02-03T01:05:27ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55470035547003A Nonlinear Implicit Fractional Equation with Caputo DerivativeAmeth Ndiaye0Département de Mathematiques, FASTEF, UCAD, Dakar, SenegalIn this paper, we study a nonlinear implicit differential equation with initial conditions. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of Banach principle. Then, another result that deals with the existence of at least one solution is delivered and some sufficient conditions for this result are established by means of the fixed point theorem of Schaefer. At the end, we discuss two examples to illustrate the applicability of the main results.http://dx.doi.org/10.1155/2021/5547003 |
| spellingShingle | Ameth Ndiaye A Nonlinear Implicit Fractional Equation with Caputo Derivative Journal of Mathematics |
| title | A Nonlinear Implicit Fractional Equation with Caputo Derivative |
| title_full | A Nonlinear Implicit Fractional Equation with Caputo Derivative |
| title_fullStr | A Nonlinear Implicit Fractional Equation with Caputo Derivative |
| title_full_unstemmed | A Nonlinear Implicit Fractional Equation with Caputo Derivative |
| title_short | A Nonlinear Implicit Fractional Equation with Caputo Derivative |
| title_sort | nonlinear implicit fractional equation with caputo derivative |
| url | http://dx.doi.org/10.1155/2021/5547003 |
| work_keys_str_mv | AT amethndiaye anonlinearimplicitfractionalequationwithcaputoderivative AT amethndiaye nonlinearimplicitfractionalequationwithcaputoderivative |