The Iterative Positive Solution for a System of Fractional q-Difference Equations with Four-Point Boundary Conditions
In this work, we investigate the following system of fractional q-difference equations with four-point boundary problems: Dqαut+ft,vt=0,0<t<1;Dqβvt+gt,ut=0,0<t<1;u0=0,u1=γ1uη1; and v0=0,v1=γ2uη2, where Dqα and Dqβ are the fractional Riemann–Liouville q-derivative of order α and β, respec...
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/3970903 |
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| author | Chuanzhi Bai Dandan Yang |
| author_facet | Chuanzhi Bai Dandan Yang |
| author_sort | Chuanzhi Bai |
| collection | DOAJ |
| description | In this work, we investigate the following system of fractional q-difference equations with four-point boundary problems: Dqαut+ft,vt=0,0<t<1;Dqβvt+gt,ut=0,0<t<1;u0=0,u1=γ1uη1; and v0=0,v1=γ2uη2, where Dqα and Dqβ are the fractional Riemann–Liouville q-derivative of order α and β, respectively, 0<q<1, 1<β≤α≤2, 0<η1,η2<1, 0<γ1η1α−1<1, and 0<γ2η2β−1<1. By virtue of monotone iterative approach, the iterative positive solutions are obtained. An example to illustrate our result is given. |
| format | Article |
| id | doaj-art-26820dc93b89454bb69f4c41a828ae54 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-26820dc93b89454bb69f4c41a828ae542025-02-03T01:27:04ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/39709033970903The Iterative Positive Solution for a System of Fractional q-Difference Equations with Four-Point Boundary ConditionsChuanzhi Bai0Dandan Yang1Department of Mathematics, Huaiyin Normal University, Huai’an, Jiangsu 223300, ChinaDepartment of Mathematics, Huaiyin Normal University, Huai’an, Jiangsu 223300, ChinaIn this work, we investigate the following system of fractional q-difference equations with four-point boundary problems: Dqαut+ft,vt=0,0<t<1;Dqβvt+gt,ut=0,0<t<1;u0=0,u1=γ1uη1; and v0=0,v1=γ2uη2, where Dqα and Dqβ are the fractional Riemann–Liouville q-derivative of order α and β, respectively, 0<q<1, 1<β≤α≤2, 0<η1,η2<1, 0<γ1η1α−1<1, and 0<γ2η2β−1<1. By virtue of monotone iterative approach, the iterative positive solutions are obtained. An example to illustrate our result is given.http://dx.doi.org/10.1155/2020/3970903 |
| spellingShingle | Chuanzhi Bai Dandan Yang The Iterative Positive Solution for a System of Fractional q-Difference Equations with Four-Point Boundary Conditions Discrete Dynamics in Nature and Society |
| title | The Iterative Positive Solution for a System of Fractional q-Difference Equations with Four-Point Boundary Conditions |
| title_full | The Iterative Positive Solution for a System of Fractional q-Difference Equations with Four-Point Boundary Conditions |
| title_fullStr | The Iterative Positive Solution for a System of Fractional q-Difference Equations with Four-Point Boundary Conditions |
| title_full_unstemmed | The Iterative Positive Solution for a System of Fractional q-Difference Equations with Four-Point Boundary Conditions |
| title_short | The Iterative Positive Solution for a System of Fractional q-Difference Equations with Four-Point Boundary Conditions |
| title_sort | iterative positive solution for a system of fractional q difference equations with four point boundary conditions |
| url | http://dx.doi.org/10.1155/2020/3970903 |
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