A Study on Controllability of a Class of Impulsive Fractional Nonlinear Evolution Equations with Delay in Banach Spaces

Under a new generalized definition of exact controllability we introduced and with a appropriately constructed time delay term in a special complete space to overcome the delay-induced-difficulty, we establish the sufficient conditions of the exact controllability for a class of impulsive fractional nonlinear evolution equations with delay by using the resolvent operator theory and the theory of nonlinear functional analysis. Nonlinearity in the system is only supposed to be continuous rather than Lipschitz continuous by contrast. The results obtained in the present work are generalizations and continuations of the recent results on this issue. Further, an example is presented to show the effectiveness of the new results.

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INTEGRAL SOLUTIONS TO A CLASS OF NONLOCAL EVOLUTION EQUATIONS

Communications in Contemporary Mathematics ◽

10.1142/s021919971000410x ◽

2010 ◽

Vol 12 (06) ◽

pp. 1031-1054 ◽

Cited By ~ 20

Author(s):

JESÚS GARCÍA-FALSET ◽

SIMEON REICH

Keyword(s):

Banach Space ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Sufficient Conditions ◽

Accretive Operator ◽

Integral Solution ◽

Nonlinear Evolution Equations ◽

Nonlocal Evolution Equations ◽

Integral Solutions

We study the existence of integral solutions to a class of nonlinear evolution equations of the form [Formula: see text] where A : D(A) ⊆ X → 2X is an m-accretive operator on a Banach space X, and f : [0, T] × X → X and [Formula: see text] are given functions. We obtain sufficient conditions for this problem to have a unique integral solution.

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LOCAL EXACT CONTROLLABILITY OF NONLINEAR EVOLUTION EQUATIONS

Recent Advances in Differential Equations ◽

10.1016/b978-0-12-186280-0.50024-4 ◽

1981 ◽

pp. 271-280 ◽

Cited By ~ 1

Author(s):

K. Magnusson ◽

A.J. Pritchard

Keyword(s):

Evolution Equations ◽

Nonlinear Evolution ◽

Exact Controllability ◽

Nonlinear Evolution Equations

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Optimality conditions for systems driven by nonlinear evolution equations

Mathematical Problems in Engineering ◽

10.1155/s1024123x95000044 ◽

1995 ◽

Vol 1 (1) ◽

pp. 27-36

Author(s):

N. Papageorgiou

Keyword(s):

Nonlinear Evolution Equation ◽

Evolution Equations ◽

Optimal Control Problems ◽

Nonlinear Evolution ◽

Sufficient Conditions ◽

Nonlinear Evolution Equations ◽

Control Problems ◽

Terminal Constraints ◽

Sufficient Conditions For Optimality ◽

Necessary And Sufficient

Using the Dubovitskii-Milyutin theory we derive necessary and sufficient conditions for optimality for a class of Lagrange optimal control problems monitored by a nonlinear evolution equation and involving initial and/or terminal constraints. An example of a parabolic control system is also included.

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Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v11i3.470 ◽

2015 ◽

Vol 11 (3) ◽

pp. 3134-3138 ◽

Cited By ~ 3

Author(s):

Mostafa Khater ◽

Mahmoud A.E. Abdelrahman

Keyword(s):

Elliptic Function ◽

Traveling Wave ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Traveling Wave Solutions ◽

Expansion Method ◽

Mathematical Physics ◽

Nonlinear Evolution Equations ◽

Jacobian Elliptic Function ◽

Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity andÂ reliability of the method are tested by its applications to the Couple Boiti-Leon-PempinelliÂ System which plays an important role in mathematical physics.

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