Analysis and Optimal Control of <i>φ</i>-Hilfer Fractional Semilinear Equations Involving Nonlocal Impulsive Conditions
The goal of this paper is to consider a new class of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-Hilfer fractional differential equation...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/11/2084 |
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| author | Sarra Guechi Rajesh Dhayal Amar Debbouche Muslim Malik |
| author_facet | Sarra Guechi Rajesh Dhayal Amar Debbouche Muslim Malik |
| author_sort | Sarra Guechi |
| collection | DOAJ |
| description | The goal of this paper is to consider a new class of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-Hilfer fractional differential equations with impulses and nonlocal conditions. By using fractional calculus, semigroup theory, and with the help of the fixed point theorem, the existence and uniqueness of mild solutions are obtained for the proposed fractional system. Symmetrically, we discuss the existence of optimal controls for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-Hilfer fractional control system. Our main results are well supported by an illustrative example. |
| first_indexed | 2024-03-10T05:00:46Z |
| format | Article |
| id | doaj.art-0d2546c344b8434590f73fafade732cd |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T05:00:46Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-0d2546c344b8434590f73fafade732cd2023-11-23T01:44:40ZengMDPI AGSymmetry2073-89942021-11-011311208410.3390/sym13112084Analysis and Optimal Control of <i>φ</i>-Hilfer Fractional Semilinear Equations Involving Nonlocal Impulsive ConditionsSarra Guechi0Rajesh Dhayal1Amar Debbouche2Muslim Malik3Department of Mathematics, Guelma University, Guelma 24000, AlgeriaSchool of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147 004, IndiaDepartment of Mathematics, Guelma University, Guelma 24000, AlgeriaSchool of Basic Sciences, Indian Institute of Technology Mandi, Kamand 175 005, IndiaThe goal of this paper is to consider a new class of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-Hilfer fractional differential equations with impulses and nonlocal conditions. By using fractional calculus, semigroup theory, and with the help of the fixed point theorem, the existence and uniqueness of mild solutions are obtained for the proposed fractional system. Symmetrically, we discuss the existence of optimal controls for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-Hilfer fractional control system. Our main results are well supported by an illustrative example.https://www.mdpi.com/2073-8994/13/11/2084<i>φ</i>-Hilfer fractional system with impulsessemigroup theorynonlocal conditionsoptimal controls |
| spellingShingle | Sarra Guechi Rajesh Dhayal Amar Debbouche Muslim Malik Analysis and Optimal Control of <i>φ</i>-Hilfer Fractional Semilinear Equations Involving Nonlocal Impulsive Conditions Symmetry <i>φ</i>-Hilfer fractional system with impulses semigroup theory nonlocal conditions optimal controls |
| title | Analysis and Optimal Control of <i>φ</i>-Hilfer Fractional Semilinear Equations Involving Nonlocal Impulsive Conditions |
| title_full | Analysis and Optimal Control of <i>φ</i>-Hilfer Fractional Semilinear Equations Involving Nonlocal Impulsive Conditions |
| title_fullStr | Analysis and Optimal Control of <i>φ</i>-Hilfer Fractional Semilinear Equations Involving Nonlocal Impulsive Conditions |
| title_full_unstemmed | Analysis and Optimal Control of <i>φ</i>-Hilfer Fractional Semilinear Equations Involving Nonlocal Impulsive Conditions |
| title_short | Analysis and Optimal Control of <i>φ</i>-Hilfer Fractional Semilinear Equations Involving Nonlocal Impulsive Conditions |
| title_sort | analysis and optimal control of i φ i hilfer fractional semilinear equations involving nonlocal impulsive conditions |
| topic | <i>φ</i>-Hilfer fractional system with impulses semigroup theory nonlocal conditions optimal controls |
| url | https://www.mdpi.com/2073-8994/13/11/2084 |
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