Existence Solutions for Implicit Fractional Relaxation Differential Equations with Impulsive Delay Boundary Conditions

Abstract

The aim of this paper is to study the existence and uniqueness of solutions for nonlinear fractional relaxation impulsive implicit delay differential equations with boundary conditions. Some findings are established by applying the Banach contraction mapping principle and the Schauder fixed-point theorem. An example is provided that illustrates the theoretical results.

Dynamics in an n-Species Lotka–Volterra Cooperative System with Delays

“…Finally, numerical simulations were employed to illustrate the effectiveness and feasibility of our results. Recently, the dynamic properties of fractional-order delay differential equations have been extensively investigated both in theory and applications [24,25]. Therefore, we have interesting future work such as the dynamical behavior on the fractional-order n-species Lotka-Volterra cooperative population systems with delays.…”

On Implicit Atangana–Baleanu–Caputo Fractional Integro-Differential Equations with Delay and Impulses

“…A delay diferential equation is a diferential equation where the time derivatives at the current time depend on the solution and possibly its derivatives at previous times. Tese models are used, among other things, in the felds of biology, economics, and mechanics, see [23]. Te delay in this diferential equation comes from the interval between the beginning of cellular production in the bone marrow and the release of mature cells into the blood.…”

Positive Solutions for Periodic Boundary Value Problems of Fractional Differential Equations with Sign-Changing Nonlinearity and Green’s Function

“…Fractional differential equations (FDEs) have attracted great interests in the past several decades as FDEs are widely used in many fields, see [1][2][3][4][5]. In recent years, many papers have investigated the existence, multiplicity and non-existence of solutions for initial value problems (IVPs) or boundary value problems (BVPs) of various classes of FDEs (conformable FDEs [6], impulsive FDEs [7], coupled system of FDEs [8][9][10], hybrid FDEs [11][12][13], fractional relaxation DEs [14], variable-order FDEs [15]); also see the references therein.…”