Ulam’s type stability of Hadamard type fractional integral equations

Abstract

In this paper, we further investigates Ulam's type stability of Hadamard type fractional integral equations on a compact interval. We explore new conditions and develop valuable techniques to overcome the difficult from the Hadamard type singular kernel and extend the previous Ulam's type stability results in [27] from [1, b] to [a, b] with a > 0 via fixed point method. Finally, two examples are given to illustrate our results.

Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

“…is a solution of the inequality (42), if and only if there exist a function g ∈ C 1−q;φ [J , R] such that:…”

“…The Ulam-Hyers stability point of view, is the vital and special type of stability that attracts many researchers in the field of mathematical analysis. Moreover, the Ulam-Hyers and Ulam-Hyers-Rassias stability of linear, implicit and nonlinear fractional differential equations were examined in [17,[35][36][37][38][39][40][41][42][43][44][45][46][47][48][49].…”

A fixed point approach to the Mittag-Leffler-Hyers-Ulam stability of a fractional integral equation

“…Recently some authors ( [11][12][13][14][15][16][17][18]) extended the Ulam stability problem from an integer-order differential equation to a fractional-order differential equation. For more results on Ulam type stability of fractional differential equations see [19][20][21][22][23].…”

Existence of Ulam Stability for Iterative Fractional Differential Equations Based on Fractional Entropy

“…Various studies are reported in [16,17]. Wang and Lin also imposed stability by utilizing the Hadamard-type fractional integral equations [18]. Recently, the stability of the sequential fractional differential equation with respect to the Miller-Ross formula was investigated on the basis of the Banach contraction mapping theorem [19].…”