Positive Solutions for a Fractional Boundary Value Problem with a Perturbation Term

Abstract

We obtain some new upper and lower estimates for the Green's function associated with a fractional boundary value problem with a perturbation term. Criteria for the existence of positive solutions of the problem are then obtained based on it.

Monotone Iterative Method for Fractional Differential Equations with Integral Boundary Conditions

“…which shows that v 0 (t) and w 0 (t) are a lower and an upper solution of (38), respectively, and v 0 (t) ≤ w 0 (t). So, (H3) holds.…”

“…It shows that (H2) holds. us, eorem 1 ensures that problem (38) has extremal solutions in [v 0 , w 0 ].…”

Asymptotic Analysis of Impulsive Dispersal Predator-Prey Systems with Markov Switching on Finite-State Space

“…Following the same argument as in [13,22,36,47], we can prove the existence and uniqueness of the global positive solution for systems (3) and (4). The proof is omitted here.…”

Existence of solutions for integral boundary value problems of mixed fractional differential equations under resonance

“…where C D α 1-and D become a popular research field. At present, many researchers study the existence of solutions of fractional differential equations such as the Riemann-Liouville fractional derivative problem at nonresonance [6][7][8][9][10][11][12][13][14][15][16], the Riemann-Liouville fractional derivative problem at resonance [17][18][19][20][21][22][23], the Caputo fractional boundary value problem [6,24,25], the Hadamard fractional boundary value problem [26][27][28], conformable fractional boundary value problems [29][30][31][32], impulsive problems [33][34][35], boundary value problems [8,[36][37][38][39][40][41][42][43], and variational structure problems [44,45].…”