Controlled Extended Branciari Quasi-b-Metric Spaces, Results, and Applications to Riesz-Caputo Fractional Differential Equations and Nonlinear Matrix Equations
We introduce the concept of controlled extended Branciari quasi-<i>b</i>-metric spaces, as well as a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">G&l...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/1/20 |
| _version_ | 1797343936538214400 |
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| author | Reena Jain Hemant Kumar Nashine Reny George |
| author_facet | Reena Jain Hemant Kumar Nashine Reny George |
| author_sort | Reena Jain |
| collection | DOAJ |
| description | We introduce the concept of controlled extended Branciari quasi-<i>b</i>-metric spaces, as well as a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">G</mi><mi>q</mi></msub></semantics></math></inline-formula>-implicit type mapping. Under this new space setting, we derive some new fixed points, periodic points, right and left Ulam–Hyers stability, right and left weak well-posed properties, and right and left weak limit shadowing results. Additionally, we use these findings to solve the fractional differential equations of a Riesz–Caputo type with integral anti-periodic boundary values, as well of nonlinear matrix equations. All ideas, results, and applications are properly illustrated with examples. |
| first_indexed | 2024-03-08T10:55:02Z |
| format | Article |
| id | doaj.art-2966546918d648c8a3354e5e607525c1 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-08T10:55:02Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-2966546918d648c8a3354e5e607525c12024-01-26T16:35:14ZengMDPI AGFractal and Fractional2504-31102023-12-01812010.3390/fractalfract8010020Controlled Extended Branciari Quasi-b-Metric Spaces, Results, and Applications to Riesz-Caputo Fractional Differential Equations and Nonlinear Matrix EquationsReena Jain0Hemant Kumar Nashine1Reny George2Mathematics Division, School of Advanced Sciences and Languages, VIT Bhopal University, Kothrikalan, Sehore 466114, Madhya Pradesh, IndiaMathematics Division, School of Advanced Sciences and Languages, VIT Bhopal University, Kothrikalan, Sehore 466114, Madhya Pradesh, IndiaDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaWe introduce the concept of controlled extended Branciari quasi-<i>b</i>-metric spaces, as well as a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">G</mi><mi>q</mi></msub></semantics></math></inline-formula>-implicit type mapping. Under this new space setting, we derive some new fixed points, periodic points, right and left Ulam–Hyers stability, right and left weak well-posed properties, and right and left weak limit shadowing results. Additionally, we use these findings to solve the fractional differential equations of a Riesz–Caputo type with integral anti-periodic boundary values, as well of nonlinear matrix equations. All ideas, results, and applications are properly illustrated with examples.https://www.mdpi.com/2504-3110/8/1/20fixed pointextended Branciari b-metric spacesRiesz–Caputo derivativeanti-periodic boundary conditionsnonlinear matrix equations |
| spellingShingle | Reena Jain Hemant Kumar Nashine Reny George Controlled Extended Branciari Quasi-b-Metric Spaces, Results, and Applications to Riesz-Caputo Fractional Differential Equations and Nonlinear Matrix Equations Fractal and Fractional fixed point extended Branciari b-metric spaces Riesz–Caputo derivative anti-periodic boundary conditions nonlinear matrix equations |
| title | Controlled Extended Branciari Quasi-b-Metric Spaces, Results, and Applications to Riesz-Caputo Fractional Differential Equations and Nonlinear Matrix Equations |
| title_full | Controlled Extended Branciari Quasi-b-Metric Spaces, Results, and Applications to Riesz-Caputo Fractional Differential Equations and Nonlinear Matrix Equations |
| title_fullStr | Controlled Extended Branciari Quasi-b-Metric Spaces, Results, and Applications to Riesz-Caputo Fractional Differential Equations and Nonlinear Matrix Equations |
| title_full_unstemmed | Controlled Extended Branciari Quasi-b-Metric Spaces, Results, and Applications to Riesz-Caputo Fractional Differential Equations and Nonlinear Matrix Equations |
| title_short | Controlled Extended Branciari Quasi-b-Metric Spaces, Results, and Applications to Riesz-Caputo Fractional Differential Equations and Nonlinear Matrix Equations |
| title_sort | controlled extended branciari quasi b metric spaces results and applications to riesz caputo fractional differential equations and nonlinear matrix equations |
| topic | fixed point extended Branciari b-metric spaces Riesz–Caputo derivative anti-periodic boundary conditions nonlinear matrix equations |
| url | https://www.mdpi.com/2504-3110/8/1/20 |
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