On a Neutral It<i>ô</i> and Arbitrary (Fractional) Orders Stochastic Differential Equation with Nonlocal Condition
In this paper, we are concerned with the combinations of the stochastic It<i>ô</i>-differential and the arbitrary (fractional) orders derivatives in a neutral differential equation with a stochastic, nonlinear, nonlocal integral condition. The existence of solutions will be proved. The s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/5/4/201 |
| _version_ | 1797504503592779776 |
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| author | Ahmed M. A. El-Sayed Hoda A. Fouad |
| author_facet | Ahmed M. A. El-Sayed Hoda A. Fouad |
| author_sort | Ahmed M. A. El-Sayed |
| collection | DOAJ |
| description | In this paper, we are concerned with the combinations of the stochastic It<i>ô</i>-differential and the arbitrary (fractional) orders derivatives in a neutral differential equation with a stochastic, nonlinear, nonlocal integral condition. The existence of solutions will be proved. The sufficient conditions for the uniqueness of the solution will be given. The continuous dependence of the unique solution will be studied. |
| first_indexed | 2024-03-10T04:05:31Z |
| format | Article |
| id | doaj.art-8b677c836d03406a86c1fe62608fdbb5 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:31Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-8b677c836d03406a86c1fe62608fdbb52023-11-23T08:23:41ZengMDPI AGFractal and Fractional2504-31102021-11-015420110.3390/fractalfract5040201On a Neutral It<i>ô</i> and Arbitrary (Fractional) Orders Stochastic Differential Equation with Nonlocal ConditionAhmed M. A. El-Sayed0Hoda A. Fouad1Faculty of Science, Alexandria University, Alexandria 21568, EgyptFaculty of Science, Alexandria University, Alexandria 21568, EgyptIn this paper, we are concerned with the combinations of the stochastic It<i>ô</i>-differential and the arbitrary (fractional) orders derivatives in a neutral differential equation with a stochastic, nonlinear, nonlocal integral condition. The existence of solutions will be proved. The sufficient conditions for the uniqueness of the solution will be given. The continuous dependence of the unique solution will be studied.https://www.mdpi.com/2504-3110/5/4/201stochastic processesstochastic differential equationIt<i>ô</i>-differentialfractional differential equationscoupled systemnonlocal stochastic integral conditions |
| spellingShingle | Ahmed M. A. El-Sayed Hoda A. Fouad On a Neutral It<i>ô</i> and Arbitrary (Fractional) Orders Stochastic Differential Equation with Nonlocal Condition Fractal and Fractional stochastic processes stochastic differential equation It<i>ô</i>-differential fractional differential equations coupled system nonlocal stochastic integral conditions |
| title | On a Neutral It<i>ô</i> and Arbitrary (Fractional) Orders Stochastic Differential Equation with Nonlocal Condition |
| title_full | On a Neutral It<i>ô</i> and Arbitrary (Fractional) Orders Stochastic Differential Equation with Nonlocal Condition |
| title_fullStr | On a Neutral It<i>ô</i> and Arbitrary (Fractional) Orders Stochastic Differential Equation with Nonlocal Condition |
| title_full_unstemmed | On a Neutral It<i>ô</i> and Arbitrary (Fractional) Orders Stochastic Differential Equation with Nonlocal Condition |
| title_short | On a Neutral It<i>ô</i> and Arbitrary (Fractional) Orders Stochastic Differential Equation with Nonlocal Condition |
| title_sort | on a neutral it i o i and arbitrary fractional orders stochastic differential equation with nonlocal condition |
| topic | stochastic processes stochastic differential equation It<i>ô</i>-differential fractional differential equations coupled system nonlocal stochastic integral conditions |
| url | https://www.mdpi.com/2504-3110/5/4/201 |
| work_keys_str_mv | AT ahmedmaelsayed onaneutralitioiandarbitraryfractionalordersstochasticdifferentialequationwithnonlocalcondition AT hodaafouad onaneutralitioiandarbitraryfractionalordersstochasticdifferentialequationwithnonlocalcondition |