Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant Functions
In this paper, we establish the existence of solutions to a nonlinear boundary value problem (BVP) of variable order at resonance. The main theorem in this study is proved with the help of generalized intervals and piecewise constant functions, in which we convert the mentioned Caputo BVP of fractio...
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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 |
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| Online Access: | https://www.mdpi.com/2504-3110/5/4/216 |
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| author | Shahram Rezapour Mohammed Said Souid Sina Etemad Zoubida Bouazza Sotiris K. Ntouyas Suphawat Asawasamrit Jessada Tariboon |
| author_facet | Shahram Rezapour Mohammed Said Souid Sina Etemad Zoubida Bouazza Sotiris K. Ntouyas Suphawat Asawasamrit Jessada Tariboon |
| author_sort | Shahram Rezapour |
| collection | DOAJ |
| description | In this paper, we establish the existence of solutions to a nonlinear boundary value problem (BVP) of variable order at resonance. The main theorem in this study is proved with the help of generalized intervals and piecewise constant functions, in which we convert the mentioned Caputo BVP of fractional variable order to an equivalent standard Caputo BVP at resonance of constant order. In fact, to use the Mawhin’s continuation technique, we have to transform the variable order BVP into a constant order BVP. We prove the existence of solutions based on the existing notions in the coincidence degree theory and Mawhin’s continuation theorem (MCTH). Finally, an example is provided according to the given variable order BVP to show the correctness of results. |
| first_indexed | 2024-03-10T04:05:23Z |
| format | Article |
| id | doaj.art-6aba2fec72894549918f9d3b408b485c |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:23Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-6aba2fec72894549918f9d3b408b485c2023-11-23T08:23:53ZengMDPI AGFractal and Fractional2504-31102021-11-015421610.3390/fractalfract5040216Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant FunctionsShahram Rezapour0Mohammed Said Souid1Sina Etemad2Zoubida Bouazza3Sotiris K. Ntouyas4Suphawat Asawasamrit5Jessada Tariboon6Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, IranDepartment of Economic Sciences, University of Tiaret, Tiaret 14035, AlgeriaDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, IranLaboratory of Mathematics, Djillali Liabes University, Sidi Bel-Abbès 22000, AlgeriaDepartment of Mathematics, University of Ioannina, 451 10 Ioannina, GreeceIntelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandIntelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandIn this paper, we establish the existence of solutions to a nonlinear boundary value problem (BVP) of variable order at resonance. The main theorem in this study is proved with the help of generalized intervals and piecewise constant functions, in which we convert the mentioned Caputo BVP of fractional variable order to an equivalent standard Caputo BVP at resonance of constant order. In fact, to use the Mawhin’s continuation technique, we have to transform the variable order BVP into a constant order BVP. We prove the existence of solutions based on the existing notions in the coincidence degree theory and Mawhin’s continuation theorem (MCTH). Finally, an example is provided according to the given variable order BVP to show the correctness of results.https://www.mdpi.com/2504-3110/5/4/216piecewise constant functionMawhin’s continuation techniquevariable orderresonanceexistence |
| spellingShingle | Shahram Rezapour Mohammed Said Souid Sina Etemad Zoubida Bouazza Sotiris K. Ntouyas Suphawat Asawasamrit Jessada Tariboon Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant Functions Fractal and Fractional piecewise constant function Mawhin’s continuation technique variable order resonance existence |
| title | Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant Functions |
| title_full | Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant Functions |
| title_fullStr | Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant Functions |
| title_full_unstemmed | Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant Functions |
| title_short | Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant Functions |
| title_sort | mawhin s continuation technique for a nonlinear bvp of variable order at resonance via piecewise constant functions |
| topic | piecewise constant function Mawhin’s continuation technique variable order resonance existence |
| url | https://www.mdpi.com/2504-3110/5/4/216 |
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