On the Generalized Hilfer Fractional Coupled Integro-Differential Systems with Multi-Point Ordinary and Fractional Integral Boundary Conditions
In this paper, we investigate a nonlinear coupled integro-differential system involving generalized Hilfer fractional derivative operators (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</m...
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MDPI AG
2024-01-01
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| author | Chayapat Sudprasert Sotiris K. Ntouyas Bashir Ahmad Ayub Samadi Jessada Tariboon |
| author_facet | Chayapat Sudprasert Sotiris K. Ntouyas Bashir Ahmad Ayub Samadi Jessada Tariboon |
| author_sort | Chayapat Sudprasert |
| collection | DOAJ |
| description | In this paper, we investigate a nonlinear coupled integro-differential system involving generalized Hilfer fractional derivative operators (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>ψ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Hilfer type) of different orders and equipped with non-local multi-point ordinary and fractional integral boundary conditions. The uniqueness results for the given problem are obtained by applying Banach’s contraction mapping principle and the Boyd–Wong fixed point theorem for nonlinear contractions. Based on the Laray–Schauder alternative and the well-known fixed-point theorem due to Krasnosel’skiĭ, the existence of solutions for the problem at hand is established under different criteria. Illustrative examples for the main results are constructed. |
| first_indexed | 2024-03-08T11:05:48Z |
| format | Article |
| id | doaj.art-e05c2bebb5b2430bb919772a137dbe33 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-08T11:05:48Z |
| publishDate | 2024-01-01 |
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| spelling | doaj.art-e05c2bebb5b2430bb919772a137dbe332024-01-26T15:03:50ZengMDPI AGAxioms2075-16802024-01-011315110.3390/axioms13010051On the Generalized Hilfer Fractional Coupled Integro-Differential Systems with Multi-Point Ordinary and Fractional Integral Boundary ConditionsChayapat Sudprasert0Sotiris K. Ntouyas1Bashir Ahmad2Ayub Samadi3Jessada Tariboon4Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandDepartment of Mathematics, University of Ioannina, 45110 Ioannina, GreeceNonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh 5315836511, IranIntelligent 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 investigate a nonlinear coupled integro-differential system involving generalized Hilfer fractional derivative operators (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>ψ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Hilfer type) of different orders and equipped with non-local multi-point ordinary and fractional integral boundary conditions. The uniqueness results for the given problem are obtained by applying Banach’s contraction mapping principle and the Boyd–Wong fixed point theorem for nonlinear contractions. Based on the Laray–Schauder alternative and the well-known fixed-point theorem due to Krasnosel’skiĭ, the existence of solutions for the problem at hand is established under different criteria. Illustrative examples for the main results are constructed.https://www.mdpi.com/2075-1680/13/1/51(<i>k</i>,<i>ψ</i>)-Hilfer fractional derivativefractional differential systemexistenceuniquenessfixed point theorems |
| spellingShingle | Chayapat Sudprasert Sotiris K. Ntouyas Bashir Ahmad Ayub Samadi Jessada Tariboon On the Generalized Hilfer Fractional Coupled Integro-Differential Systems with Multi-Point Ordinary and Fractional Integral Boundary Conditions Axioms (<i>k</i>,<i>ψ</i>)-Hilfer fractional derivative fractional differential system existence uniqueness fixed point theorems |
| title | On the Generalized Hilfer Fractional Coupled Integro-Differential Systems with Multi-Point Ordinary and Fractional Integral Boundary Conditions |
| title_full | On the Generalized Hilfer Fractional Coupled Integro-Differential Systems with Multi-Point Ordinary and Fractional Integral Boundary Conditions |
| title_fullStr | On the Generalized Hilfer Fractional Coupled Integro-Differential Systems with Multi-Point Ordinary and Fractional Integral Boundary Conditions |
| title_full_unstemmed | On the Generalized Hilfer Fractional Coupled Integro-Differential Systems with Multi-Point Ordinary and Fractional Integral Boundary Conditions |
| title_short | On the Generalized Hilfer Fractional Coupled Integro-Differential Systems with Multi-Point Ordinary and Fractional Integral Boundary Conditions |
| title_sort | on the generalized hilfer fractional coupled integro differential systems with multi point ordinary and fractional integral boundary conditions |
| topic | (<i>k</i>,<i>ψ</i>)-Hilfer fractional derivative fractional differential system existence uniqueness fixed point theorems |
| url | https://www.mdpi.com/2075-1680/13/1/51 |
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