Existence of solutions for fractional Langevin equation with infinite-point boundary conditions

On fractional Langevin equation involving two fractional orders in different intervals

“…Recently, the existence of solutions of the initial and boundary value problems for nonlinear fractional equations are extensively studied. For example, see Kosmatov [18], Li et al [24], Deng et al [9], Gorka et al [12], Lakshmikantham et al [23], Zhou et al [34] and Guo et al [13].…”

On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders

“…Lim et al [27] introduced a new form of Langevin equation containing two different fractional orders, which has made it possible to investigate fractal processes in a more flexible environment. For some recent works on fractional Langevin equation, see the papers [28][29][30][31][32][33][34][35][36] and the references cited therein.…”

Langevin equation involving one fractional order with three-point boundary conditions

“…With different unit intervals of values to two fractional orders α and β, many authors introduced their works. For instance, [3,4,22,24,25] concerned with m − 1 < α m and n − 1 < β n, m, n ∈ N, [1,15,21] concerned with 0 < α, β 1, [2,7,12,27] concerned with 0 < α 1 and 1 < β 2, [5,11] concerned with 1 < α 2 and 0 < β 1, and Gao et al [8] concerned with 1 < α, β 2.…”