scholarly journals Hilfer-type fractional differential switched inclusions with noninstantaneous impulsive and nonlocal conditions

2018 ◽  
Vol 23 (6) ◽  
pp. 921-941 ◽  
Author(s):  
JinRong Wang ◽  
Ahmed Gamal Ibrahim ◽  
Donal O’Regan
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Continuous Functions ◽  
Inclusion Problem ◽  
Nonlocal Problems ◽  
Hausdorff Measure Of Noncompactness ◽  
New Class ◽  
Fractional Differential

In this paper, we study a new class of nonlocal problems for noninstantaneous impulsive Hilfer-type fractional differential switched inclusions in Banach spaces. First, we introduce a mild solution formula for this noninstantaneous impulsive inclusion problem. Second, we show the existence of mild solutions using the Hausdorff measure of noncompactness on the space of piecewise weighted continuous functions. Finally, an example is provided to illustrate the theory.

SEMILINEAR NONLOCAL PROBLEMS WITHOUT THE ASSUMPTIONS OF COMPACTNESS IN BANACH SPACES

2010 ◽  
Vol 08 (02) ◽  
pp. 211-225 ◽  
Author(s):  
XINGMEI XUE
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Differential System ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Nonlocal Problems ◽  
Hausdorff Measure Of Noncompactness ◽  
Nonlocal Initial Conditions

In this paper, we study the semilinear differential equations with nonlocal initial conditions in the separable Banach spaces. We derive conditions expressed in terms of the Hausdorff measure of noncompactness under which the mild solutions exit. For illustration, a partial integral differential system is worked out.

scholarly journals Solvability of infinite systems of fractional differential equations in the spaces of tempered sequences

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5519-5530 ◽  
Author(s):  
Anupam Das ◽  
Bipan Hazarika ◽  
Ravi Agarwal ◽  
Hemant Nashine
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Existence Of Solution ◽  
Hausdorff Measure Of Noncompactness ◽  
Infinite Systems ◽  
Fractional Differential

In this paper we discuss the existence of solution of infinite systems of fractional differential equations with the help of Hausdorff measure of noncompactness and Meir-Keeler fixed point theorem in the tempered sequence spaces. We provide examples to established the applicability of our results.

Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness

2012 ◽  
Vol 15 (4) ◽  
Author(s):  
Kexue Li ◽  
Jigen Peng ◽  
Jinghuai Gao
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Kuratowski Measure Of Noncompactness ◽  
Condensing Operator ◽  
Fractional Differential

AbstractIn this paper, we study the existence of mild solutions for a class of semilinear fractional differential equations with nonlocal conditions in Banach spaces. The results are obtained by using convex-power condensing operator and fixed point theory. An example is presented to illustrate the main result.

scholarly journals Global attracting solutions to Hilfer fractional differential inclusions of Sobolev type with noninstantaneous impulses and nonlocal conditions

2019 ◽  
Vol 24 (5) ◽  
Author(s):  
JinRong Wang ◽  
Ahmed Gamal Ibrahim ◽  
Donal O’Regan
Keyword(s):  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Nonlocal Conditions ◽  
Continuous Functions ◽  
Sobolev Type ◽  
Unbounded Interval ◽  
Fractional Differential ◽  
Noninstantaneous Impulses

In this paper, we establish the existence of decay mild solutions on an unbounded interval of nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and involving the Hilfer derivative. Our argument uses fixed point theorems, semigroup theory, multi-functions and a measure of noncompactness on the space of piecewise weighted continuous functions defined on an unbounded interval. An example is provided to illustrate our results.

scholarly journals Analysis and Optimal Control of φ-Hilfer Fractional Semilinear Equations Involving Nonlocal Impulsive Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2084
Author(s):  
Sarra Guechi ◽  
Rajesh Dhayal ◽  
Amar Debbouche ◽  
Muslim Malik
Keyword(s):  
Mild Solutions ◽  
Semigroup Theory ◽  
Nonlocal Conditions ◽  
Optimal Controls ◽  
Impulsive Conditions ◽  
Semilinear Equations ◽  
New Class ◽  
Fractional Differential ◽  
The Fixed Point Theorem ◽  
Fractional Control

The goal of this paper is to consider a new class of φ-Hilfer fractional differential equations with impulses and nonlocal conditions. By using fractional calculus, semigroup theory, and with the help of the fixed point theorem, the existence and uniqueness of mild solutions are obtained for the proposed fractional system. Symmetrically, we discuss the existence of optimal controls for the φ-Hilfer fractional control system. Our main results are well supported by an illustrative example.

On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 451-460 ◽  
Author(s):  
Mohammed Belmekki ◽  
Kheira Mekhalfi
Keyword(s):  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Kuratowski Measure Of Noncompactness ◽  
State Dependent ◽  
State Dependent Delay ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

scholarly journals Solvability of control problem for fractional nonlinear differential inclusions with nonlocal conditions

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Alka Chadha ◽  
Rathinasamy Sakthivel ◽  
Swaroop Nandan Bora
Keyword(s):  
Differential Inclusions ◽  
Approximate Controllability ◽  
Measure Of Noncompactness ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Nonlinear Differential Inclusions ◽  
Approximately Controllable ◽  
Fractional Differential

In this paper, we study the approximate controllability of nonlocal fractional differential inclusions involving the Caputo fractional derivative of order q ∈ (1,2) in a Hilbert space. Utilizing measure of noncompactness and multivalued fixed point strategy, a new set of sufficient conditions is obtained to ensure the approximate controllability of nonlocal fractional differential inclusions when the multivalued maps are convex. Precisely, the results are developed under the assumption that the corresponding linear system is approximately controllable.  

scholarly journals Measure of noncompactness of operators and matrices on the spacescandc0

2006 ◽  
Vol 2006 ◽  
pp. 1-5 ◽  
Author(s):  
Bruno De Malafosse ◽  
Eberhard Malkowsky ◽  
Vladimir Rakocevic
Keyword(s):  
Linear Operator ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Hausdorff Measure Of Noncompactness ◽  
Necessary And Sufficient

In this note, using the Hausdorff measure of noncompactness, necessary and sufficient conditions are formulated for a linear operator and matrices between the spacescandc0to be compact. Among other things, some results of Cohen and Dunford are recovered.

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