Multiple Positive Solutions for a System of Fractional Order BVP with <i>p</i>-Laplacian Operators and Parameters
In this paper, we investigate the existence of positive solutions to a system of fractional differential equations that include the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-10-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/12/10/974 |
| _version_ | 1797574755223601152 |
|---|---|
| author | Abdullah Ali H. Ahmadini Mahammad Khuddush Sabbavarapu Nageswara Rao |
| author_facet | Abdullah Ali H. Ahmadini Mahammad Khuddush Sabbavarapu Nageswara Rao |
| author_sort | Abdullah Ali H. Ahmadini |
| collection | DOAJ |
| description | In this paper, we investigate the existence of positive solutions to a system of fractional differential equations that include the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>r</mi><mn>1</mn></msub><mo>,</mo><msub><mi>r</mi><mn>2</mn></msub><mo>,</mo><msub><mi>r</mi><mn>3</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian operator, three-point boundary conditions, and various fractional derivatives. We use a combination of techniques, including cone expansion and compression of the functional type, and the Leggett–Williams fixed point theorem, to prove the existence of positive solutions. Finally, we provide two examples to illustrate our main results. |
| first_indexed | 2024-03-10T21:26:50Z |
| format | Article |
| id | doaj.art-d655a1b4c06b496fa77bd18a31dff621 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T21:26:50Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-d655a1b4c06b496fa77bd18a31dff6212023-11-19T15:38:42ZengMDPI AGAxioms2075-16802023-10-01121097410.3390/axioms12100974Multiple Positive Solutions for a System of Fractional Order BVP with <i>p</i>-Laplacian Operators and ParametersAbdullah Ali H. Ahmadini0Mahammad Khuddush1Sabbavarapu Nageswara Rao2Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi ArabiaDepartment of Mathematics, Chegg India Pvt. Ltd., Andhra Pradesh, Visakhapatnam 530002, IndiaDepartment of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi ArabiaIn this paper, we investigate the existence of positive solutions to a system of fractional differential equations that include the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>r</mi><mn>1</mn></msub><mo>,</mo><msub><mi>r</mi><mn>2</mn></msub><mo>,</mo><msub><mi>r</mi><mn>3</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian operator, three-point boundary conditions, and various fractional derivatives. We use a combination of techniques, including cone expansion and compression of the functional type, and the Leggett–Williams fixed point theorem, to prove the existence of positive solutions. Finally, we provide two examples to illustrate our main results.https://www.mdpi.com/2075-1680/12/10/974fractional derivativepositive solutionsboundary value problems<i>p</i>-Laplacianparameters |
| spellingShingle | Abdullah Ali H. Ahmadini Mahammad Khuddush Sabbavarapu Nageswara Rao Multiple Positive Solutions for a System of Fractional Order BVP with <i>p</i>-Laplacian Operators and Parameters Axioms fractional derivative positive solutions boundary value problems <i>p</i>-Laplacian parameters |
| title | Multiple Positive Solutions for a System of Fractional Order BVP with <i>p</i>-Laplacian Operators and Parameters |
| title_full | Multiple Positive Solutions for a System of Fractional Order BVP with <i>p</i>-Laplacian Operators and Parameters |
| title_fullStr | Multiple Positive Solutions for a System of Fractional Order BVP with <i>p</i>-Laplacian Operators and Parameters |
| title_full_unstemmed | Multiple Positive Solutions for a System of Fractional Order BVP with <i>p</i>-Laplacian Operators and Parameters |
| title_short | Multiple Positive Solutions for a System of Fractional Order BVP with <i>p</i>-Laplacian Operators and Parameters |
| title_sort | multiple positive solutions for a system of fractional order bvp with i p i laplacian operators and parameters |
| topic | fractional derivative positive solutions boundary value problems <i>p</i>-Laplacian parameters |
| url | https://www.mdpi.com/2075-1680/12/10/974 |
| work_keys_str_mv | AT abdullahalihahmadini multiplepositivesolutionsforasystemoffractionalorderbvpwithipilaplacianoperatorsandparameters AT mahammadkhuddush multiplepositivesolutionsforasystemoffractionalorderbvpwithipilaplacianoperatorsandparameters AT sabbavarapunageswararao multiplepositivesolutionsforasystemoffractionalorderbvpwithipilaplacianoperatorsandparameters |