Existence and uniqueness of monotone positive solutions for fractional higher-order BVPs

2020 ◽  
Vol 50 (2) ◽  
pp. 733-745
Author(s):  
Mi Zhou
Keyword(s):  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Higher Order ◽  
Monotone Positive Solutions

Higher-order singular multi-point boundary-value problems on time scales

2011 ◽  
Vol 54 (2) ◽  
pp. 345-361 ◽  
Author(s):  
Abdulkadir Dogan ◽  
John R. Graef ◽  
Lingju Kong
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Operator Theory ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Higher Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Mixed Monotone Operator ◽  
Monotone Operator Theory

AbstractWe study classes of higher-order singular boundary-value problems on a time scale $\mathbb{T}$ with a positive parameter λ in the differential equations. A homeomorphism and homomorphism ø are involved both in the differential equation and in the boundary conditions. Criteria are obtained for the existence and uniqueness of positive solutions. The dependence of positive solutions on the parameter λ is studied. Applications of our results to special problems are also discussed. Our analysis mainly relies on the mixed monotone operator theory. The results here are new, even in the cases of second-order differential and difference equations.

scholarly journals Positive Solutions to Nonlinear Higher-Order Nonlocal Boundary Value Problems for Fractional Differential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Mujeeb Ur Rehman ◽  
Rahmat Ali Khan
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Nonlocal Boundary Value Problems ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We study existence of positive solutions to nonlinear higher-order nonlocal boundary value problems corresponding to fractional differential equation of the type , , . , , , , where, , , , the boundary parameters and is the Caputo fractional derivative. We use the classical tools from functional analysis to obtain sufficient conditions for the existence and uniqueness of positive solutions to the boundary value problems. We also obtain conditions for the nonexistence of positive solutions to the problem. We include examples to show the applicability of our results.

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