UNIQUENESS OF SOLUTIONS FOR AN INTEGRAL BOUNDARY VALUE PROBLEM WITH FRACTIONAL Q-DIFFERENCES

Yaqiong Cui; Shugui Kang; Huiqin Chen

doi:10.11948/2018.524

2018 Volume 8 Issue 2

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Yaqiong Cui, Shugui Kang, Huiqin Chen. UNIQUENESS OF SOLUTIONS FOR AN INTEGRAL BOUNDARY VALUE PROBLEM WITH FRACTIONAL Q-DIFFERENCES[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 524-531. doi: 10.11948/2018.524

Citation:

Yaqiong Cui, Shugui Kang, Huiqin Chen. UNIQUENESS OF SOLUTIONS FOR AN INTEGRAL BOUNDARY VALUE PROBLEM WITH FRACTIONAL Q-DIFFERENCES[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 524-531. doi: 10.11948/2018.524

UNIQUENESS OF SOLUTIONS FOR AN INTEGRAL BOUNDARY VALUE PROBLEM WITH FRACTIONAL Q-DIFFERENCES

School of Mathematics and Computer Science, Shanxi Datong University, Datong 037009, China

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Abstract

Abstract

This paper deals with uniqueness of solutions for integral boundary value problem {8<:(D_q^αu)(t) + f(t,u(t))=0,t ∈ (0,1),u(0)=D_qu(0)=0,u(1)=λ ∫₀¹ u(s)d_qs,where α ∈ (2,3], λ ∈ (0;[α]_q), D_q_α denotes the q-fractional differential operator of order α. By using the iterative method and one new fixed point theorem, we obtain that there exist a unique nontrivial solution and a unique positive solution.
- Fractional q-difference equation /
- integral boundary value condition /
- the first eigenvalue /
- uniqueness of solutions
MSC: O175.1;O175.8

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