Solvability of impulsive periodic boundary value problems for higher order fractional differential equations

Abstract

A class of periodic boundary value problems for higher order fractional differential equations with impulse effects is considered. We first convert the problem to an equivalent integral equation. Then, using a fixed-point theorem in Banach space, we establish existence results of solutions for this kind of boundary value problem for impulsive singular higher order fractional differential equations. Two examples are presented to illustrate the efficiency of the results obtained. Mathematics Subject Classification

Periodic boundary value problems for higher‐order fractional differential systems

“…Then scalar FDE with asymptotically constant nonlinearities are investigated leading to Landesman‐Lazer–type conditions . Similar problems used different methods are presented in other studies …”

“…According to the Cauchy criteria, the sequence of functions {x k } ∞ k=0 , defined by (16), uniformly converges in [0, T] to the limit function x ∞ . Passing j → ∞ in (22), we get the estimate (19). As all functions of the sequence (16) satisfy periodic boundary conditions, the limit function (17) satisfies them as well.…”

“…12 Similar problems used different methods are presented in other studies. [13][14][15][16][17][18][19][20][21][22][23][24]…”

Existence and Uniqueness Theorems for a Fractional Differential Equation with Impulsive Effect under Band-Like Integral Boundary Conditions

“…e research results of fractional differential equations with integral boundary conditions are also quite rich, and the research on those questions remains as a hotpot among many scholars in recent years. We refer readers to see [13][14][15][16] and the reference therein.…”

“…Accordingly, the conclusions we reached are extensive results compared with the reference [4][5][6][7][15][16][17][18][19][20] and a meaningful supplement to the theory of impulsive fractional differential equations.…”