A Survey on Recent Results on Lyapunov-Type Inequalities for Fractional Differential Equations
نویسندگان
چکیده
This survey paper is concerned with some of the most recent results on Lyapunov-type inequalities for fractional boundary value problems involving a variety derivative operators and conditions. Our work deals Caputo, Riemann-Liouville, ?-Caputo, ?-Hilfer, hybrid, Caputo-Fabrizio, Hadamard, Katugampola, Hilfer-Katugampola, p-Laplacian, proportional operators.
منابع مشابه
global results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Lyapunov-type Inequalities for Differential Equations
Let us consider the linear boundary value problem u′′(x) + a(x)u(x) = 0, x ∈ (0, L), u′(0) = u′(L) = 0, (0.1) where a ∈ Λ0 and Λ0 is defined by Λ0 = {a ∈ L∞(0, L) \ {0} : Z L 0 a(x) dx ≥ 0, (0.1) has nontrivial solutions}. Classical Lyapunov inequality states that Z L 0 a(x) dx > 4/L for any function a ∈ Λ0, where a(x) = max{a(x), 0}. The constant 4/L is optimal. Let us note that Lyapunov inequ...
متن کاملLyapunov-type integral inequalities for certain higher order differential equations
In this paper, we obtain Liapunov-type integral inequalities for certain nonlinear, nonhomogeneous differential equations of higher order with without any restriction on the zeros of their higher-order derivatives of the solutions by using elementary analysis. As an applications of our results, we show that oscillatory solutions of the equation converge to zero as t → ∞. Using these inequalitie...
متن کاملLyapunov–type Inequalities for Third–order Linear Differential Equations
In this paper, we obtain new Lyapunov-type inequalities for the third-order linear differential equation x′′′ + q(t)x = 0 . Our work provides the sharpest results in the literature and makes corrections to those in a recently published paper [1]. Based on the above, we further establish new Lyapunov-type inequalities for more general third-order linear differential equations. Moreover, by combi...
متن کاملLyapunov-type Inequalities for Odd Order Linear Differential Equations
In this article, we obtain Lyapunov-type inequalities for certain odd order linear boundary-value problems. Our inequalities involve integrals of both q+(t) and q−(t) in addition to that of |q(t)|. The Green’s function for even order boundary-value problems plays a key role in our proofs. Also, using the Fredholm alternative theorem, we obtain a criterion for the existence and uniqueness of sol...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fractal and fractional
سال: 2022
ISSN: ['2504-3110']
DOI: https://doi.org/10.3390/fractalfract6050273