Existence of solution of infinite systems of inhomogeneous wave equations using Hausdorff measure of noncompactness

2020 ◽  
Vol 5 (4) ◽  
pp. 1315-1324
Author(s):  
Anupam Das ◽  
Bipan Hazarika ◽  
M. Mursaleen ◽  
Poom Kumam
Keyword(s):  
Hausdorff Measure ◽  
Wave Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solution ◽  
Hausdorff Measure Of Noncompactness ◽  
Inhomogeneous Wave ◽  
Infinite Systems

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.

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.

scholarly journals Existence Results for an Impulsive Neutral Fractional Integrodifferential Equation with Infinite Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Alka Chadha ◽  
Dwijendra N. Pandey
Keyword(s):  
Banach Space ◽  
Mild Solution ◽  
Hausdorff Measure ◽  
Integrodifferential Equation ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Existence Results ◽  
Hausdorff Measure Of Noncompactness ◽  
Arbitrary Banach Space ◽  
Fractional Integrodifferential Equation

We consider an impulsive neutral fractional integrodifferential equation with infinite delay in an arbitrary Banach spaceX. The existence of mild solution is established by using solution operator and Hausdorff measure of noncompactness.

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.

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