We obtain the Hyers-Ulam stability and modified Hyers-Ulam stability for the equations of the formg(x+p)=φ(x)g(x) in the following settings: |g(x+p)−φ(x)g(x)| ≤ δ, |g(x+p)−φ(x)g(x)| ≤φ(x), |(g(x+p)/φ(x)g(x))−1| ≤ψ(x). As a consequence we obtain the stability theorems for the gamma functional equation.

Abstract In this paper, we consider fractional neutral differential equations with multipoint boundary value conditions involving Hadamard derivatives and integrals. We obtain the existence uniqueness of solution equation by using several fixed point theorems, also Ulam–Hyers stability solution. addition, study inclusion problem prove when multivalued map has convex values. give examples to ill...

In this paper, the existence of solution and its stability to fractional boundary value problem (FBVP) were investigated for an implicit nonlinear differential equation (VOFDE) variable order. All criteria solutions in our establishments derived via Krasnoselskii’s fixed point theorem sequel, Ulam–Hyers–Rassias (U-H-R) is checked. An illustrative example presented at end paper validate findings.

Fractional calculus is nowadays an efficient tool in modelling many interesting nonlinear phenomena. This study investigates, a novel way, the Ulam–Hyers (HU) and Ulam–Hyers–Rassias (HUR) stability of differential equations with general conformable derivative (GCD). In our analysis, we employ some version Banach fixed-point theory (FPT). this generalize several earlier results. Two examples are...

In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo operators, nonperiodic nonlocal integral boundary conditions. The results presented in study establish existence, uniqueness, Hyers–Ulam (HU) stability of solution to proposed equation. We achieved our main result by using Banach contraction mapping principle Kraso...

Abstract In this article, we study a class of nonlinear fractional differential equation for the existence and uniqueness positive solution Hyers–Ulam-type stability. To proceed work, utilize tools fixed point theory analysis to investigate concern theory. We convert into an integral alternative form with help Greens function. Using desired function, studied proposed equation. next section auth...

we show that  higher derivations on a hilbert$c^{*}-$module associated with the cauchy functional equation satisfying generalized hyers--ulam stability.

Abstract In this research work, a class of multi-term fractional pantograph differential equations (FODEs) subject to antiperiodic boundary conditions (APBCs) is considered. The ensuing problem involves proportional type delay terms and constitutes subclass known as pantograph. On using fixed point theorems due Banach Schaefer, some sufficient are developed for the existence uniqueness solution...

ABSTRACT. In this paper, Ulam stability and data dependence for fractional differential equations with Caputo fractional derivative of order α are studied. We present four types of Ulam stability results for the fractional differential equation in the case of 0 < α < 1 and b = +∞ by virtue of the Henry-Gronwall inequality. Meanwhile, we give an interesting data dependence results for the fracti...

In this paper, the authors established the generalized Ulam Hyers stability of additive functional equation    