Abstract
In this paper, using the idea of separated intervals in non-instantaneous impulsive equations, we initiate the study of initial value problems for mixed-order ordinary and fractional differential equations with instantaneous impulsive effects. Existence and uniqueness results are established via standard fixed point theorems. Examples illustrating the main results are also presented.
Highlights
1 Introduction and preliminaries Fractional differential equations have been shown to be very useful in the study of models of many phenomena in various fields of science and engineering, such as physics, chemistry, biology, signal and image processing, biophysics, blood flow phenomena, control theory, economics, aerodynamics, and fitting of experimental data
Impulsive differential equations are used to describe many practical dynamical systems, including evolutionary processes characterized by abrupt changes of the state at certain instants
Such processes are naturally seen in biology, physics, engineering, and so forth
Summary
Introduction and preliminariesFractional differential equations have been shown to be very useful in the study of models of many phenomena in various fields of science and engineering, such as physics, chemistry, biology, signal and image processing, biophysics, blood flow phenomena, control theory, economics, aerodynamics, and fitting of experimental data. In this paper, we study the existence and uniqueness of solutions for two new classes of instantaneous impulses of mixed-order ordinary differential equations, as well as, fractional differential equations with initial conditions. The first problem for mixed-order ordinary impulsive differential equations is presented by
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