Ulam-Hyers stability of fractional impulsive differential equations

Abstract

In this paper, we first prove the existence and uniqueness for a fractional differential equation with time delay and finite impulses on a compact interval. Secondly, Ulam-Hyers stability of the equation is established by Picard operator and abstract Gronwall's inequality.

Approximation of an Additive ϱ1,ϱ2-Random Operator Inequality

“…Recently, some authors have published some papers on stability of functional equations in several spaces by the direct method and the fixed point method, for example, Banach spaces [6][7][8], fuzzy Menger normed algebras [9], fuzzy normed spaces [10], non-Archimedean random Lie C * -algebras [11], non-Archimedean random normed spaces [12], random multinormed space [13], random lattice normed spaces, and random normed algebras [14,15]. In [16,17], the authors studied the stability problem for fractional equations. Next, Cȃdariu et al [18][19][20] applied the fixed point method to solve the stability problem, and their work was continued by Keltouma et al [21], Park et al [22,23], Jung and Lee [24], and Brzdȩk and Ciepliński [25], see also [26,27].…”

Approximation of Mixed Euler-Lagrange σ -Cubic-Quartic Functional Equation in Felbin’s Type f-NLS

“…Recently, the stability problems of several functional equations (FEs) have been extensively investigated by a number of authors [4,[9][10][11][12][13][14][15][16][17][18][19][20] in Felbin type f-NLS. Our method helps to solve some new problems of stability and approximation of functional equations [21][22][23][24][25][26][27][28] in Felbin type f-NLS.…”