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

Yaqiong Cui | Zendy; Shugui Kang | Zendy; Huiqin Chen | Zendy

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

Author(s) -

Yaqiong Cui,

Shugui Kang,

Huiqin Chen

Publication year - 2018

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2018.524

Subject(s) - uniqueness , mathematics , combinatorics , boundary value problem , order (exchange) , fixed point , mathematical analysis , physics , mathematical physics , economics , finance

This paper deals with uniqueness of solutions for integral boundary value problem (D α q u)(t) + f(t, u(t)) = 0, t ∈ (0, 1), u(0) = Dqu(0) = 0, u(1) = λ ∫ 1 0 u(s)dqs, where α ∈ (2, 3], λ ∈ (0, [α]q), D q 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.

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