Systems of Riemann–Liouville Fractional Differential Equations with <i>ρ</i>-Laplacian Operators and Nonlocal Coupled Boundary Conditions
In this paper, we study the existence of positive solutions for a system of fractional differential equations with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math>&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/10/610 |
| _version_ | 1797473211288387584 |
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| author | Alexandru Tudorache Rodica Luca |
| author_facet | Alexandru Tudorache Rodica Luca |
| author_sort | Alexandru Tudorache |
| collection | DOAJ |
| description | In this paper, we study the existence of positive solutions for a system of fractional differential equations with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-Laplacian operators, Riemann–Liouville derivatives of diverse orders and general nonlinearities which depend on several fractional integrals of differing orders, supplemented with nonlocal coupled boundary conditions containing Riemann–Stieltjes integrals and varied fractional derivatives. The nonlinearities from the system are continuous nonnegative functions and they can be singular in the time variable. We write equivalently this problem as a system of integral equations, and then we associate an operator for which we are looking for its fixed points. The main results are based on the Guo–Krasnosel’skii fixed point theorem of cone expansion and compression of norm type. |
| first_indexed | 2024-03-09T20:11:37Z |
| format | Article |
| id | doaj.art-6156850b64674afbbd4fb925591b8753 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T20:11:37Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-6156850b64674afbbd4fb925591b87532023-11-24T00:12:26ZengMDPI AGFractal and Fractional2504-31102022-10-0161061010.3390/fractalfract6100610Systems of Riemann–Liouville Fractional Differential Equations with <i>ρ</i>-Laplacian Operators and Nonlocal Coupled Boundary ConditionsAlexandru Tudorache0Rodica Luca1Department of Computer Science and Engineering, Gh. Asachi Technical University, 700050 Iasi, RomaniaDepartment of Mathematics, Gh. Asachi Technical University, 700506 Iasi, RomaniaIn this paper, we study the existence of positive solutions for a system of fractional differential equations with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-Laplacian operators, Riemann–Liouville derivatives of diverse orders and general nonlinearities which depend on several fractional integrals of differing orders, supplemented with nonlocal coupled boundary conditions containing Riemann–Stieltjes integrals and varied fractional derivatives. The nonlinearities from the system are continuous nonnegative functions and they can be singular in the time variable. We write equivalently this problem as a system of integral equations, and then we associate an operator for which we are looking for its fixed points. The main results are based on the Guo–Krasnosel’skii fixed point theorem of cone expansion and compression of norm type.https://www.mdpi.com/2504-3110/6/10/610Riemann–Liouville fractional differential equationsnonlocal coupled boundary conditionssingular functionspositive solutionsmultiplicity |
| spellingShingle | Alexandru Tudorache Rodica Luca Systems of Riemann–Liouville Fractional Differential Equations with <i>ρ</i>-Laplacian Operators and Nonlocal Coupled Boundary Conditions Fractal and Fractional Riemann–Liouville fractional differential equations nonlocal coupled boundary conditions singular functions positive solutions multiplicity |
| title | Systems of Riemann–Liouville Fractional Differential Equations with <i>ρ</i>-Laplacian Operators and Nonlocal Coupled Boundary Conditions |
| title_full | Systems of Riemann–Liouville Fractional Differential Equations with <i>ρ</i>-Laplacian Operators and Nonlocal Coupled Boundary Conditions |
| title_fullStr | Systems of Riemann–Liouville Fractional Differential Equations with <i>ρ</i>-Laplacian Operators and Nonlocal Coupled Boundary Conditions |
| title_full_unstemmed | Systems of Riemann–Liouville Fractional Differential Equations with <i>ρ</i>-Laplacian Operators and Nonlocal Coupled Boundary Conditions |
| title_short | Systems of Riemann–Liouville Fractional Differential Equations with <i>ρ</i>-Laplacian Operators and Nonlocal Coupled Boundary Conditions |
| title_sort | systems of riemann liouville fractional differential equations with i ρ i laplacian operators and nonlocal coupled boundary conditions |
| topic | Riemann–Liouville fractional differential equations nonlocal coupled boundary conditions singular functions positive solutions multiplicity |
| url | https://www.mdpi.com/2504-3110/6/10/610 |
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