Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions
In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann–Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions <inline-formula>&...
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MDPI AG
2021-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/1/107 |
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| author | Daliang Zhao Juan Mao |
| author_facet | Daliang Zhao Juan Mao |
| author_sort | Daliang Zhao |
| collection | DOAJ |
| description | In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann–Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions <inline-formula><math display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><mi>g</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></semantics></math></inline-formula> in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann–Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green’s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results. |
| first_indexed | 2024-03-09T05:31:14Z |
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| id | doaj.art-5a630a0aa75145afae0e002b08a31dca |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T05:31:14Z |
| publishDate | 2021-01-01 |
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| series | Symmetry |
| spelling | doaj.art-5a630a0aa75145afae0e002b08a31dca2023-12-03T12:32:04ZengMDPI AGSymmetry2073-89942021-01-0113110710.3390/sym13010107Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value ConditionsDaliang Zhao0Juan Mao1School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, ChinaDepartment of Basic Courses, Shandong Polytechnic, Jinan 250104, ChinaIn this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann–Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions <inline-formula><math display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><mi>g</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></semantics></math></inline-formula> in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann–Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green’s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results.https://www.mdpi.com/2073-8994/13/1/107fractional differential equationssingularitycoupled integral boundary value conditionsconefixed point theorem |
| spellingShingle | Daliang Zhao Juan Mao Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions Symmetry fractional differential equations singularity coupled integral boundary value conditions cone fixed point theorem |
| title | Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions |
| title_full | Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions |
| title_fullStr | Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions |
| title_full_unstemmed | Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions |
| title_short | Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions |
| title_sort | positive solutions for a class of nonlinear singular fractional differential systems with riemann stieltjes coupled integral boundary value conditions |
| topic | fractional differential equations singularity coupled integral boundary value conditions cone fixed point theorem |
| url | https://www.mdpi.com/2073-8994/13/1/107 |
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