UNIQUENESS AND PARAMETER DEPENDENCE OF POSITIVE SOLUTIONS TO HIGHER ORDER BOUNDARY VALUE PROBLEMS WITH FRACTIONAL <i>Q</i>-DERIVATIVES

John R. Graef; Lingju Kong; Qingkai Kong; Min Wang

doi:10.11948/2013003

2013 Volume 3 Issue 1

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John R. Graef, Lingju Kong, Qingkai Kong, Min Wang. UNIQUENESS AND PARAMETER DEPENDENCE OF POSITIVE SOLUTIONS TO HIGHER ORDER BOUNDARY VALUE PROBLEMS WITH FRACTIONAL Q-DERIVATIVES[J]. Journal of Applied Analysis & Computation, 2013, 3(1): 21-35. doi: 10.11948/2013003

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John R. Graef, Lingju Kong, Qingkai Kong, Min Wang. UNIQUENESS AND PARAMETER DEPENDENCE OF POSITIVE SOLUTIONS TO HIGHER ORDER BOUNDARY VALUE PROBLEMS WITH FRACTIONAL Q-DERIVATIVES[J]. Journal of Applied Analysis & Computation, 2013, 3(1): 21-35. doi: 10.11948/2013003

UNIQUENESS AND PARAMETER DEPENDENCE OF POSITIVE SOLUTIONS TO HIGHER ORDER BOUNDARY VALUE PROBLEMS WITH FRACTIONAL Q-DERIVATIVES

1 Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA;
2 Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA

Abstract

Abstract

The authors study a class of nonlinear higher order boundary value problem with fractional q-derivatives and dependence on a positive parameter λ. The existence, uniqueness, and dependence of positive solutions on λ are discussed. Two sequences are constructed so that they converge uniformly to the unique solution of the problems. Two examples are included in the paper. Numerical computations of the examples confirm their theoretical results.
- Fractional q-calculus /
- boundary value problems /
- positive solutions /
- existence /
- uniqueness
MSC: 39A13;34B18;34A08

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