IMPULSIVE INEQUALITIES FOR MULTI-DELAY JUMP CONDITIONS

Abstract. In this paper, we establish some new impulsive inequalities for multi-delay jump conditions in which the jump conditions depend on multi-point of the states at past times. These inequalities can be used as basic tools in the study of differential equations with nonlocal impulse effects. Some examples are given to illustrate the application of our results

Periodic Boundary Value Problems for First-Order Impulsive Functional Integrodifferential Equations with Integral-Jump Conditions

By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive functional integrodifferential equations with integral-jump conditions. An example is also given to illustrate our results

Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions

We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder’s degree theory. Enlightening examples illustrating the obtained results are also presented

On Impulsive Implicit ψ-Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation

In this paper, we investigate the existence and Ulam–Hyers–Rassias stability results for a class of boundary value problems for implicit ψ-Caputo fractional differential equations with non-instantaneous impulses involving both retarded and advanced arguments. The results are based on the Banach contraction principle and Krasnoselskii’s fixed point theorem. In addition, the Ulam–Hyers–Rassias stability result is proved using the nonlinear functional analysis technique. Finally, illustrative examples are given to validate our main results

Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions

We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach's fixed point theorem, Krasnoselskii's fixed point theorem, Leray-Schauder's nonlinear alternative, and Leray-Schauder's degree theory. Enlightening examples illustrating the obtained results are also presented

Analysis of Impulsive Boundary Value Pantograph Problems via Caputo Proportional Fractional Derivative under Mittag–Leffler Functions

This manuscript investigates an extended boundary value problem for a fractional pantograph differential equation with instantaneous impulses under the Caputo proportional fractional derivative with respect to another function. The solution of the proposed problem is obtained using Mittag–Leffler functions. The existence and uniqueness results of the proposed problem are established by combining the well-known fixed point theorems of Banach and Krasnoselskii with nonlinear functional techniques. In addition, numerical examples are presented to demonstrate our theoretical analysis