Positive Solutions for Nonlinear Caputo Type Fractional q-Difference Equations with Integral Boundary Conditions
Abstract
:1. Introduction
2. Preliminaries
- (H1)
- and , where , , and
- (i)
- , and , ,
- (ii)
- , and , .
- (i)
- and , for all ;
- (ii)
- , for all ;
- (iii)
- , for all with .
3. Main Results
- (H2)
- There exist two constants and with such that
- (H3)
- and (particularly, and );
- (H4)
- and (particularly, and ).
- (H5)
- and (particularly, ),
- (H6)
- There exists satisfying , .
- (H7)
- and (particularly, ),
- (H8)
- There exists satisfying , .
- (H9)
- , for all , and ,
- (H10)
- , for all , and ,
- (H11)
- , for all , and .
4. Some Examples
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Yang, W.; Qin, Y. Positive Solutions for Nonlinear Caputo Type Fractional q-Difference Equations with Integral Boundary Conditions. Mathematics 2016, 4, 63. https://doi.org/10.3390/math4040063
Yang W, Qin Y. Positive Solutions for Nonlinear Caputo Type Fractional q-Difference Equations with Integral Boundary Conditions. Mathematics. 2016; 4(4):63. https://doi.org/10.3390/math4040063
Chicago/Turabian StyleYang, Wengui, and Yaping Qin. 2016. "Positive Solutions for Nonlinear Caputo Type Fractional q-Difference Equations with Integral Boundary Conditions" Mathematics 4, no. 4: 63. https://doi.org/10.3390/math4040063