Ulam-type stability for a class of implicit fractional differential equations with non-instantaneous integral impulses and boundary condition
نویسندگان
چکیده
In this paper, we investigate four different types of Ulam stability, i.e., Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of nonlinear implicit fractional differential equations with non-instantaneous integral impulses and nonlinear integral boundary condition. We also establish certain conditions for the existence and uniqueness of solutions for such a class of fractional differential equations using Caputo fractional derivative. The arguments are based on generalized Diaz-Margolis’s fixed point theorem. We provide two examples, which shows the validity of our main results.
منابع مشابه
Mittag-Leffler-Hyers-Ulam Stability of Fractional Differential Equation
In this article, we study the Mittag-Leffler-Hyers-Ulam and Mittag-Leffler-Hyers-Ulam-Rassias stability of a class of fractional differential equation with boundary condition.
متن کاملThe new implicit finite difference scheme for two-sided space-time fractional partial differential equation
Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...
متن کاملHyers-Ulam Stability of Non-Linear Volterra Integro-Delay Dynamic System with Fractional Integrable Impulses on Time Scales
This manuscript presents Hyers-Ulam stability and Hyers--Ulam--Rassias stability results of non-linear Volterra integro--delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem is used for obtaining existence and uniqueness of solutions. By means of abstract Gr"{o}nwall lemma, Gr"{o}nwall's inequality on time scales, we establish Hyers-Ulam stabi...
متن کاملExistence of positive solution to a class of boundary value problems of fractional differential equations
This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...
متن کاملNumerical solution for boundary value problem of fractional order with approximate Integral and derivative
Approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. In this paper with central difference approximation and Newton Cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. Three...
متن کامل