A new type of three dimensional metric spaces with applications to fractional differential equations
In this manuscript, we introduce a three dimension metric type spaces so called $ J $-metric spaces. We prove the existence and uniqueness of a fixed point for self mappings in such spaces with different types of contractions. We use our result to prove the existence and uniqueness of a solution of...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2022-08-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022980?viewType=HTML |
| Summary: | In this manuscript, we introduce a three dimension metric type spaces so called $ J $-metric spaces. We prove the existence and uniqueness of a fixed point for self mappings in such spaces with different types of contractions. We use our result to prove the existence and uniqueness of a solution of the following fractional differential equations such as
$ \mathcal{(P)}:\left\{ \begin{array}{ccl} D^{\lambda}x(t) & = & f(t,x(t)) = Fx(t) \;{\rm{ if }}\; t\in I_0 = (0,T] \\ x(0) & = & x(T) = r \\ \end{array} \right\} . $
Moreover, we present other applications to systems of linear equations and Fredholm type integral equation. |
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| ISSN: | 2473-6988 |