Nonexistence of positive solutions for a system of coupled fractional boundary value problems

Abstract

We investigate the nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with coupled integral boundary conditions. MSC: 34A08; 45G15

Existence and Nonexistence of Positive Solutions for Coupled Riemann-Liouville Fractional Boundary Value Problems

“…Proof. In a similar manner as in the proof of Theorem 3.1 from [11], we can show that 0 = min{1/(4 1 ), 1/(4 1 )} and 0 = min{1/(4 2 ), 1/(4 2 )}, where = ∫ Theorem 11. Assume that ( 1) and ( 2) hold, and ∈ (0, 1).…”

“…2 Discrete Dynamics in Nature and Society were investigated in [10,11] (where and are nonnegative and nonsingular functions) and in [12] (where = = 1 and ( , , V) and ( , , V) are replaced bỹ( , V) and̃( , ), respectively, with̃and̃nonnegative functions, singular or not). In this paper, Green's functions associated with problem ( )-( ), the inequalities satisfied by these functions, and the cone defined in the proof of the main results are different than the corresponding ones that the authors used in [10][11][12] for problem ( )-( 1 ). Existence results for the positive solutions of problem ( )-( ), where and are signchanging functions which may be singular at = 0 or = 1 and satisfy some different assumptions than those used in this paper, were obtained in [13].…”

Positive Solutions for a System of Fractional Differential Equations with Parameters and Coupled Multi-point Boundary Conditions

“…By using (6), (7) and Theorem 2.1, i), we conclude that has a fixed point ( , ) ∈ ∩ (Ω 2 ̅̅̅̅ ∖ Ω 1 ) such In what follows, for 0 , 0 , ∞ , ∞ ∈ (0, ∞) and numbers 1 , 2 ∈ [0,1], 3 , 4 ∈ (0,1), ∈ [0,1] and ∈ (0,1), we define the numbers By using similar arguments as those used in the proof of Theorem 3.1 (see also [5]) we obtain the following result.…”

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

“…The interest in this topic results from the applicability of nonlocal and integral conditions in mathemati-cal modeling of many real world situations arising in applied and biological sciences. For details and examples, see [11][12][13][14][15][16][17][18][19][20][21][22][23] and the references cited therein.…”