492 research outputs found
On the Nonlinear Impulsive --Hilfer Fractional Differential Equations
In this paper, we consider the nonlinear -Hilfer impulsive fractional
differential equation. Our main objective is to derive the formula for the
solution and examine the existence and uniqueness of results. The acquired
results are extended to the nonlocal -Hilfer impulsive fractional
differential equation. We gave an applications to the outcomes we procured.
Further, examples are provided in support of the results we got.Comment: 2
A unified existence theory for evolution equations and systems under nonlocal conditions
We investigate the effect of nonlocal conditions expressed by linear
continuous mappings over the hypotheses which guarantee the existence of global
mild solutions for functional-differential equations in a Banach space. A
progressive transition from the Volterra integral operator associated to the
Cauchy problem, to Fredholm type operators appears when the support of the
nonlocal condition increases from zero to the entire interval of the problem.
The results are extended to systems of equations in a such way that the system
nonlinearities behave independently as much as possible and the support of the
nonlocal condition may differ from one variable to another.Comment: 19 page
Existence of solutions of abstract fractional impulsive semilinear evolution equations
In this paper we prove the existence of solutions of fractional impulsive semilinear evolution equations in Banach spaces. A nonlocal Cauchy problem is discussed for the evolution equations. The results are obtained using fractional calculus and fixed point theorems. An example is provided to illustrate the theory
Existence of Mild Solutions for Semilinear Impulsive Functional Mixed Integro-differential Equations with Nonlocal Conditions
In this paper, we prove the existence, uniqueness and continuous dependence of initial data on mild solutions of first order semilinear functional impulsive mixed integro-differential equations with nonlocal condition in general Banach spaces. The results are obtained by using the semigroup theory and Banach contraction theorem
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