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Positive Solutions to Nonlinear Higher-Order Nonlocal Boundary Value Problems for Fractional Differential Equations
oleh: Mujeeb Ur Rehman, Rahmat Ali Khan
Format: | Article |
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Diterbitkan: | Wiley 2010-01-01 |
Deskripsi
We study existence of positive solutions to nonlinear higher-order nonlocal boundary value problems corresponding to fractional differential equation of the type πππΏ0+π’(π‘)+π(π‘,π’(π‘))=0, π‘β(0,1), 0<π‘<1. π’(1)=π½π’(π)+π2, π’ξ (0)=πΌπ’ξ (π)βπ1, π’ξ (0)=0, π’ξ (0)=0β―π’(πβ1)(0)=0, where, πβ1<πΏ<π, π(β₯3)ββ, 0<π,πΌ,π½<1, the boundary parameters π1,π2ββ+ and ππ·πΏ0+ 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.