FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

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A singular boundary value problem for nonlinear differential equations of fractional order (2009, background): “In [2], Bai and Lü considered the boundary value problem of fractional order D 0+u(t)+ f (t, u(t))= 0, t ∈ (0,1), u(0)= u(1)= 0, where 1 < α ≤ 2 and f : [0,1] × [0,∞)→ [0,∞) is a continuous function.”
Existence and uniqueness of solutions for a fractional boundary value problem on a graph (2014, unknown): “Many results on the existence, uniqueness, multiplicity, and nonexistence of solutions for fractional differential equations subject to various boundary conditions (BCs) have been obtained; see for example [1, 2, 4, 7, 8, 11, 12, 13, 14, 15, 16, 17, 19, 20, 25, 26, 27].”
Positive solutions for boundary value problems of nonlinear fractional differential equations (2011, background): “< M( 6η Γ(α) + 2η + (t2 − t1 ) Γ(1 + α) ) In order to estimate t2 − t1 , we can apply a method used in [7]; that is, for η ≤ t1 < t2 ≤ 1, by means of mean value theorem of differentiation, we have t2 − t1 ≤ α(t2 − t1) < αη ≤ 2η for 0 ≤ t1 < η, t2 < 2η, we have t2 − t1 ≤ t2 < (2η) ≤ 2η .”