Abstract
In this article, the existence and uniqueness of generalized nonlinear impulsive evolution equation is derived. The proposed system is modeled with nonlinear perturbed force which changes after every impulse. The Banach contraction principle is applied to prove the existence and uniqueness of mild solution. The existence and uniqueness of classical solution is obtained by fixing the impulse and the conditions in which mild solution becomes classical solution also obtained. Finally an example is illustrated to the effectiveness of main results.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
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- Numerical Treatment of the Modified Burgers’ Equation via Backward Differentiation Formulas of Orders Two and Three
- Return Mapping Algorithms (RMAs) for Two-Yield Surface Thermoviscoplastic Models Using the Consistent Tangent Operator
- Synchronization of Multiple Mechanical Oscillators Under Noisy Measurements Signals and Mismatch Parameters
- Nonlinear Wave Modulation in Nanorods Using Nonlocal Elasticity Theory
- Asymptotic Behavior of the Fractional Order three Species Prey–Predator Model
- Continuous Dependence on Data for Solutions of Fractional Extended Fisher–Kolmogorov Equation
- L-stable Explicit Nonlinear Method with Constant and Variable Step-size Formulation for Solving Initial Value Problems
- Weakness and Mittag–Leffler Stability of Solutions for Time-Fractional Keller–Segel Models
- Stability Analysis of Multi-point Boundary Value Problem for Sequential Fractional Differential Equations with Non-instantaneous Impulses
- Existence and Uniqueness of Classical and Mild Solutions of Generalized Impulsive Evolution Equation
- A Collocation Method Based on Jacobi and Fractional Order Jacobi Basis Functions for Multi-Dimensional Distributed-Order Diffusion Equations
- Two-Dimensional Legendre Wavelets for Solving Variable-Order Fractional Nonlinear Advection-Diffusion Equation with Variable Coefficients
Articles in the same Issue
- Frontmatter
- Numerical Treatment of the Modified Burgers’ Equation via Backward Differentiation Formulas of Orders Two and Three
- Return Mapping Algorithms (RMAs) for Two-Yield Surface Thermoviscoplastic Models Using the Consistent Tangent Operator
- Synchronization of Multiple Mechanical Oscillators Under Noisy Measurements Signals and Mismatch Parameters
- Nonlinear Wave Modulation in Nanorods Using Nonlocal Elasticity Theory
- Asymptotic Behavior of the Fractional Order three Species Prey–Predator Model
- Continuous Dependence on Data for Solutions of Fractional Extended Fisher–Kolmogorov Equation
- L-stable Explicit Nonlinear Method with Constant and Variable Step-size Formulation for Solving Initial Value Problems
- Weakness and Mittag–Leffler Stability of Solutions for Time-Fractional Keller–Segel Models
- Stability Analysis of Multi-point Boundary Value Problem for Sequential Fractional Differential Equations with Non-instantaneous Impulses
- Existence and Uniqueness of Classical and Mild Solutions of Generalized Impulsive Evolution Equation
- A Collocation Method Based on Jacobi and Fractional Order Jacobi Basis Functions for Multi-Dimensional Distributed-Order Diffusion Equations
- Two-Dimensional Legendre Wavelets for Solving Variable-Order Fractional Nonlinear Advection-Diffusion Equation with Variable Coefficients