22 documents found, page 1 of 3
Stabilities of Ulam-Hyers type for a class of nonlinear fractional differential...
Castro, L. P.; Simões, A. M.Motivated by the knowledge of the existence of continuous solutions of a certain fractional boundary value problem with integral boundary conditions, we present in here --in a unified manner-- new sufficient conditions to conclude the existence and uniqueness of continuously differentiable solutions to this fractional boundary value problem and analyse its stability in the sense of Ulam-Hyers and Ulam-Hyers-Ras...
On the stability of bessel differential equation
Jung, Soon-Mo; Simões, A. M.; Ponmana Selvan, A.; Roh, JaiokUsing power series method, Kim and Jung (2007) investigated the Hyers-Ulam stability of the Bessel differential equation, x^2y′′(x)+xy′(x)+(x^2−α^2)y(x) = 0, of order non-integral number α > 0. Also Bicer and Tunc (2017) obtained new sufficient conditions guaranteeing the Hyers-Ulam stability of Bessel differential equation of order zero. In this paper, by classical integral method we will investigate the stabi...
A wave diffraction problem with higher order impedance boundary conditions
Simões, A. M.In this paper, we consider an impedance boundary transmission problem for the Helmholtz equation originated by a problem of wave diffraction by an infinite strip with higher order imperfect boundary conditions. Operator theoretical methods and relations between operators are built to deal with the problem and, as consequence, a transparent interpretation of the problem in an operator theory framework are associ...
A Hyers-Ulam stability analysis for classes of Bessel equations
Castro, L. P.; Simões, A. M.Mathematical modeling helps us to better understand different natural phenomena. Modeling is most of the times based on the consideration of appropriate equations (or systems of equations). Here, differential equations are well-known to be very useful instruments when building mathematical models - specially because that the use of derivatives offers several interpretations associated with real life laws. Diffe...
New sufficient conditions to ulam stabilities for a class of higher order integ...
Simões, A. M.; Carapau, F.; Correia, P.In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class of higher order integro-differential equations. In particular, we consider a new kind of stability, the sigma-semi-Hyers-Ulam stability, which is in some sense between the Hyers-Ulam and the Hyers-Ulam-Rassias stabilities. These new sufficient conditions result from the application of the Banach ...
A Hyers-Ulam stability analysis for classes of Bessel equations
Castro, L. P.; Simões, A. M.Mathematical modeling helps us to better understand different natural phenomena. Modeling is most of the times based on the consideration of appropriate equations (or systems of equations). Here, differential equations are well-known to be very useful instruments when building mathematical models { specially because that the use of derivatives offers several interpretations associated with real life laws. Diffe...
Hyers-Ulam stability of a certain Fredholm integral equation
Simões, A. M.; Selvan, PonmanaIn this paper, by using Fixed point Theorem we establish the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of certain homogeneous Fredholm Integral equation of the second kind and non-homogeneous equation.
Hyers-Ulam and Hyers-Ulam-Rassias stability for a class of integro-differential...
Castro, L. P.; Simões, A. M.We analyse different kinds of stabilities for a class of very general nonlinear integro-differential equations of Volterra type within appropriate metric spaces. Sufficient conditions are obtained in view to guarantee Hyers-Ulam stability and Hyers-Ulam-Rassias stability for such a class of integro-differential equations. We will consider the different situations of having the integrals defined on finite and in...
Hyers-Ulam and Hyers-Ulam-Rassias Stability for a Class of Integro-Differential...
Castro, L. P.; Simões, A. M.The concept of stability for functional, differential, integral and integro-differential equations has been studied in a quite extensive way during the last six decades and has earned particular interest due to their great number of applications (see [1, 3, 5, 6, 8–16, 18–23, 26] and the references therein). [...]
VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstr...
Simões, A. M.; Nunes, Célia; Inácio, Ilda; Grilo, Luis; Carapau, FernandoThis Workshop takes place at the University of Beira Interior, located in the beautiful city of Covilhã, Portugal. The host institution, as well as the Polytechnic Institute of Tomar and the University of Évora have committed themselves tothis challenge, hoping that the final result may exceed the expectations of the participants ,sponsors and organizers. [...]