Existence and Uniqueness Results of Fractional Differential Inclusions and Equations in Sobolev Fractional Spaces
In this work, by using the iterative method, we discuss the existence and uniqueness of solutions for multiterm fractional boundary value problems. Next, we examine some existence and uniqueness returns for semilinear fractional differential inclusions and equations for multiterm problems by using s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/11/1063 |
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| author | Safia Meftah Elhabib Hadjadj Mohamad Biomy Fares Yazid |
| author_facet | Safia Meftah Elhabib Hadjadj Mohamad Biomy Fares Yazid |
| author_sort | Safia Meftah |
| collection | DOAJ |
| description | In this work, by using the iterative method, we discuss the existence and uniqueness of solutions for multiterm fractional boundary value problems. Next, we examine some existence and uniqueness returns for semilinear fractional differential inclusions and equations for multiterm problems by using some notions and properties on set-valued maps and give some examples to explain our main results. We explore and use in this paper the fundamental properties of set-valued maps, which are needed for the study of differential inclusions. It began only in the mid-1900s, when mathematicians realized that their uses go far beyond a mere generalization of single-valued maps. |
| first_indexed | 2024-03-09T17:01:10Z |
| format | Article |
| id | doaj.art-031342ac5dfe4c678e716ad4bd2bb8e8 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T17:01:10Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-031342ac5dfe4c678e716ad4bd2bb8e82023-11-24T14:29:04ZengMDPI AGAxioms2075-16802023-11-011211106310.3390/axioms12111063Existence and Uniqueness Results of Fractional Differential Inclusions and Equations in Sobolev Fractional SpacesSafia Meftah0Elhabib Hadjadj1Mohamad Biomy2Fares Yazid3Laboratory of Operator Theory, EDP and Applications, University of Echahid Hamma Lakhdar, El Oued 39000, AlgeriaLaboratory of Operator Theory, EDP and Applications, University of Echahid Hamma Lakhdar, El Oued 39000, AlgeriaDepartment of Management Information Systems, Faculty of Business Administration in Ar-Rass, Qassim University, Buraydah 52571, Saudi ArabiaLaboratory of Pure and Applied Mathematics, Amar Telidji University, Laghouat 03000, AlgeriaIn this work, by using the iterative method, we discuss the existence and uniqueness of solutions for multiterm fractional boundary value problems. Next, we examine some existence and uniqueness returns for semilinear fractional differential inclusions and equations for multiterm problems by using some notions and properties on set-valued maps and give some examples to explain our main results. We explore and use in this paper the fundamental properties of set-valued maps, which are needed for the study of differential inclusions. It began only in the mid-1900s, when mathematicians realized that their uses go far beyond a mere generalization of single-valued maps.https://www.mdpi.com/2075-1680/12/11/1063semilinear fractional differential inclusionboundary value problemfixed-point theoremset-valued mapsiterative methodsRiemann–Liouville operator |
| spellingShingle | Safia Meftah Elhabib Hadjadj Mohamad Biomy Fares Yazid Existence and Uniqueness Results of Fractional Differential Inclusions and Equations in Sobolev Fractional Spaces Axioms semilinear fractional differential inclusion boundary value problem fixed-point theorem set-valued maps iterative methods Riemann–Liouville operator |
| title | Existence and Uniqueness Results of Fractional Differential Inclusions and Equations in Sobolev Fractional Spaces |
| title_full | Existence and Uniqueness Results of Fractional Differential Inclusions and Equations in Sobolev Fractional Spaces |
| title_fullStr | Existence and Uniqueness Results of Fractional Differential Inclusions and Equations in Sobolev Fractional Spaces |
| title_full_unstemmed | Existence and Uniqueness Results of Fractional Differential Inclusions and Equations in Sobolev Fractional Spaces |
| title_short | Existence and Uniqueness Results of Fractional Differential Inclusions and Equations in Sobolev Fractional Spaces |
| title_sort | existence and uniqueness results of fractional differential inclusions and equations in sobolev fractional spaces |
| topic | semilinear fractional differential inclusion boundary value problem fixed-point theorem set-valued maps iterative methods Riemann–Liouville operator |
| url | https://www.mdpi.com/2075-1680/12/11/1063 |
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