Multi-Point Boundary Value Problems for (<i>k</i>, <i>ϕ</i>)-Hilfer Fractional Differential Equations and Inclusions
In this paper we initiate the study of boundary value problems for fractional differential equations and inclusions involving <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>...
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MDPI AG
2022-03-01
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| Online Access: | https://www.mdpi.com/2075-1680/11/3/110 |
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| author | Jessada Tariboon Ayub Samadi Sotiris K. Ntouyas |
| author_facet | Jessada Tariboon Ayub Samadi Sotiris K. Ntouyas |
| author_sort | Jessada Tariboon |
| collection | DOAJ |
| description | In this paper we initiate the study of boundary value problems for fractional differential equations and inclusions involving <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>ϕ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Hilfer fractional derivative of order in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>]</mo></mrow></semantics></math></inline-formula>. In the single-valued case the existence and uniqueness results are established by using classical fixed-point theorems, such as Banach, Krasnoselskiĭ and Leray-Schauder. In the multivalued case we consider both cases, when the right-hand side has convex or non-convex values. In the first case, we apply the Leray–Schauder nonlinear alternative for multivalued maps, and in the second, the Covit–Nadler fixed-point theorem for multivalued contractions. All results are well illustrated by numerical examples. |
| first_indexed | 2024-03-09T13:50:53Z |
| format | Article |
| id | doaj.art-400c52dce7a14852a5973cd80c067dbd |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T13:50:53Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-400c52dce7a14852a5973cd80c067dbd2023-11-30T20:50:01ZengMDPI AGAxioms2075-16802022-03-0111311010.3390/axioms11030110Multi-Point Boundary Value Problems for (<i>k</i>, <i>ϕ</i>)-Hilfer Fractional Differential Equations and InclusionsJessada Tariboon0Ayub Samadi1Sotiris K. Ntouyas2Intelligent and Nonlinear Dynamic Innovations, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandDepartment of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh, IranDepartment of Mathematics, University of Ioannina, 451 10 Ioannina, GreeceIn this paper we initiate the study of boundary value problems for fractional differential equations and inclusions involving <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>ϕ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Hilfer fractional derivative of order in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>]</mo></mrow></semantics></math></inline-formula>. In the single-valued case the existence and uniqueness results are established by using classical fixed-point theorems, such as Banach, Krasnoselskiĭ and Leray-Schauder. In the multivalued case we consider both cases, when the right-hand side has convex or non-convex values. In the first case, we apply the Leray–Schauder nonlinear alternative for multivalued maps, and in the second, the Covit–Nadler fixed-point theorem for multivalued contractions. All results are well illustrated by numerical examples.https://www.mdpi.com/2075-1680/11/3/110(<i>k</i>, <i>ϕ</i>)-Hilfer fractional derivativeRiemann-Liouville fractional derivativeCaputo fractional derivativeexistenceuniquenessfixed point theorems |
| spellingShingle | Jessada Tariboon Ayub Samadi Sotiris K. Ntouyas Multi-Point Boundary Value Problems for (<i>k</i>, <i>ϕ</i>)-Hilfer Fractional Differential Equations and Inclusions Axioms (<i>k</i>, <i>ϕ</i>)-Hilfer fractional derivative Riemann-Liouville fractional derivative Caputo fractional derivative existence uniqueness fixed point theorems |
| title | Multi-Point Boundary Value Problems for (<i>k</i>, <i>ϕ</i>)-Hilfer Fractional Differential Equations and Inclusions |
| title_full | Multi-Point Boundary Value Problems for (<i>k</i>, <i>ϕ</i>)-Hilfer Fractional Differential Equations and Inclusions |
| title_fullStr | Multi-Point Boundary Value Problems for (<i>k</i>, <i>ϕ</i>)-Hilfer Fractional Differential Equations and Inclusions |
| title_full_unstemmed | Multi-Point Boundary Value Problems for (<i>k</i>, <i>ϕ</i>)-Hilfer Fractional Differential Equations and Inclusions |
| title_short | Multi-Point Boundary Value Problems for (<i>k</i>, <i>ϕ</i>)-Hilfer Fractional Differential Equations and Inclusions |
| title_sort | multi point boundary value problems for i k i i ϕ i hilfer fractional differential equations and inclusions |
| topic | (<i>k</i>, <i>ϕ</i>)-Hilfer fractional derivative Riemann-Liouville fractional derivative Caputo fractional derivative existence uniqueness fixed point theorems |
| url | https://www.mdpi.com/2075-1680/11/3/110 |
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