Nontrivial Solutions for a System of Fractional q-Difference Equations Involving q-Integral Boundary Conditions

Abstract

In this paper, we study the existence of nontrivial solutions for a system of fractional q-difference equations involving q-integral boundary conditions, and we use the topological degree to establish our main results by considering the first eigenvalue of some associated linear integral operators.

Application of some special operators on the analysis of a new generalized fractional Navier problem in the context of q-calculus

“…It is easy to find that lim inf t→∞ (tψ(t)) > 0 and ψ(t) < t for all t > 0. Now by(15) and(20) we get (1.88 + 2) 0.26 (2 -1.88) + 1 0.26 (1.41 + 1) 0.26 (1.88 + 2) 0.26 (2 -1.88) ≈ 2.082361, and χ 1 = ζ 1 ≈ 0.319646 and χ 2 = ζ 2 ≈ 0.297361. For every μ 1 , μ 2 , μ1 , μ2 ∈ R, we have H d M t, μ 1 (t), μ 2 (t) , M t, μ1 (t), μ2 (t)…”

“…and then further investigations were performed by Al-Salam and Agarwal [15,16]. Some fascinating studies into IVPs and BVPs with equations involving q-operators are available in [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Monotone Iterative Schemes for Positive Solutions of a Fractional q -Difference Equation with Integral Boundary Conditions on the Half-Line

“…e fractional q-difference calculus had its origin in the works by Al-Salam [3] and Agarwal [4]. Due to the development of the fractional differential equations, fractional q-differential equations, regarded as fractional analogue of q-difference equations, have been studied by several researchers, especially, about the existence of the solutions for the boundary value problems (see [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and the references therein).…”

Nontrivial Solutions for the 2 n th Lidstone Boundary Value Problem

“…Under some appropriate conditions involving the eigenvalues of the relevant linear operators, they utilized the topological degree to obtain a nontrivial solution for (5). In [13], the authors adopted the similar method in [12] to study the existence of nontrivial solutions for the following system of fractional q-difference equations with q-integral boundary conditions:…”