Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation
In this work, we introduce various Darbo-type F£-contractions, and utilizing these contractions, we present some fixed point theorems. Moreover, we introduce a Darbo-type F£-expanding mapping and prove fixed point theorems under the Darbo-type F£-expanding mapping. Employing our results, we check th...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/4581035 |
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| _version_ | 1832551712449101824 |
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| author | Mian Bahadur Zada Muhammad Sarwar Thabet Abdeljawad Fahd Jarad |
| author_facet | Mian Bahadur Zada Muhammad Sarwar Thabet Abdeljawad Fahd Jarad |
| author_sort | Mian Bahadur Zada |
| collection | DOAJ |
| description | In this work, we introduce various Darbo-type F£-contractions, and utilizing these contractions, we present some fixed point theorems. Moreover, we introduce a Darbo-type F£-expanding mapping and prove fixed point theorems under the Darbo-type F£-expanding mapping. Employing our results, we check the existence of a solution to the nonlinear fractional-order differential equation under the integral type boundary conditions. For its validity, an appropriate example is given. |
| format | Article |
| id | doaj-art-f7ea1cf74bd14f57860d6e16281b8d09 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-f7ea1cf74bd14f57860d6e16281b8d092025-02-03T06:00:49ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/45810354581035Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential EquationMian Bahadur Zada0Muhammad Sarwar1Thabet Abdeljawad2Fahd Jarad3Department of Mathematics, University of Malakand, Chakdara Dir (L), Khyber Pakhtunkhw, PakistanDepartment of Mathematics, University of Malakand, Chakdara Dir (L), Khyber Pakhtunkhw, PakistanDepartment of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaDepartment of Mathematics, Cankaya University, 06790 Etimesgut, Ankara, TurkeyIn this work, we introduce various Darbo-type F£-contractions, and utilizing these contractions, we present some fixed point theorems. Moreover, we introduce a Darbo-type F£-expanding mapping and prove fixed point theorems under the Darbo-type F£-expanding mapping. Employing our results, we check the existence of a solution to the nonlinear fractional-order differential equation under the integral type boundary conditions. For its validity, an appropriate example is given.http://dx.doi.org/10.1155/2020/4581035 |
| spellingShingle | Mian Bahadur Zada Muhammad Sarwar Thabet Abdeljawad Fahd Jarad Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation Journal of Function Spaces |
| title | Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation |
| title_full | Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation |
| title_fullStr | Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation |
| title_full_unstemmed | Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation |
| title_short | Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation |
| title_sort | generalized darbo type f contraction and f expansion and its applications to a nonlinear fractional order differential equation |
| url | http://dx.doi.org/10.1155/2020/4581035 |
| work_keys_str_mv | AT mianbahadurzada generalizeddarbotypefcontractionandfexpansionanditsapplicationstoanonlinearfractionalorderdifferentialequation AT muhammadsarwar generalizeddarbotypefcontractionandfexpansionanditsapplicationstoanonlinearfractionalorderdifferentialequation AT thabetabdeljawad generalizeddarbotypefcontractionandfexpansionanditsapplicationstoanonlinearfractionalorderdifferentialequation AT fahdjarad generalizeddarbotypefcontractionandfexpansionanditsapplicationstoanonlinearfractionalorderdifferentialequation |