Results 11 to 20 of about 293 (71)

Solvability of Implicit Fractional Order Integral Equation in ℓp(1 ≤ p<∞) Space via Generalized Darbo’s Fixed Point Theorem

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
We present a generalization of Darbo’s fixed point theorem in this article, and we use it to investigate the solvability of an infinite system of fractional order integral equations in ℓp(1 ≤ p<∞) space. The fundamental tool in the presentation of our proofs is the measure of noncompactness (mnc) approach.
Inzamamul Haque, Javid Ali, M. Mursaleen, Reny George   +3 more
wiley   +1 more source

Existence of Solutions for Nonlinear Integral Equations in Tempered Sequence Spaces via Generalized Darbo‐Type Theorem

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
Two concepts—one of Darbo‐type theorem and the other of Banach sequence spaces—play a very important and active role in ongoing research on existence problems. We first demonstrate the generalized Darbo‐type fixed point theorems involving the concept of continuous functions.
S. A. Mohiuddine, Anupam Das, Abdullah Alotaibi, Santosh Kumar   +3 more
wiley   +1 more source

Solution of a Fractional Integral Equation Using the Darbo Fixed Point Theorem

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
The concept of measure of noncompactness in a Banach space is used in this paper to extend some tripled fixed point theorems. We prove the existence of fractional integral equation solutions using a generalized Darbo fixed point theorem. To demonstrate the validity of the main result, an example is provided.
Bhuban Chandra Deuri, Marija V. Paunović, Anupam Das, Vahid Parvaneh, Ali Jaballah   +4 more
wiley   +1 more source

Global Attractor for Second‐Order Nonlinear Evolution Differential Inclusions

Complexity, Volume 2021, Issue 1, 2021., 2021
In this paper, we address the model of global attractor formulated in the form of evolution differential inclusions with second order in Banach spaces. Firstly, based on the fixed point theorem, the existence result of mild solutions is deduced. Then, by implementing the measure of noncompactness, the existence of global attractor associated with m ...
Guangwang Su, Funing Lin, Ahmed Mostafa Khalil   +2 more
wiley   +1 more source

Some New Results for the Sobolev‐Type Fractional Order Delay Systems with Noncompact Semigroup

Journal of Function Spaces, Volume 2020, Issue 1, 2020., 2020
The topological structure of solution sets for the Sobolev‐type fractional order delay systems with noncompact semigroup is studied. Based on a fixed point principle for multivalued maps, the existence result is obtained under certain mild conditions.
Qiaomin Xiang, Pengxian Zhu, Mark A. McKibben   +2 more
wiley   +1 more source

Existence Results for Generalized Bagley‐Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions

Journal of Function Spaces, Volume 2018, Issue 1, 2018., 2018
In this article, we prove the existence of solutions for the generalized Bagley‐Torvik type fractional order differential inclusions with nonlocal conditions. It allows applying the noncompactness measure of Hausdorff, fractional calculus theory, and the nonlinear alternative for Kakutani maps fixed point theorem to obtain the existence results under ...
Lizhen Chen, Gang Li, Liguang Wang
wiley   +1 more source

Existence of the Mild Solution for Impulsive Semilinear Differential Equation

International Journal of Partial Differential Equations, Volume 2014, Issue 1, 2014., 2014
We study the existence of solutions of impulsive semilinear differential equation in a Banach space X in which impulsive condition is not instantaneous. We establish the existence of a mild solution by using the Hausdorff measure of noncompactness and a fixed point theorem for the convex power condensing operator.
Alka Chadha, Dwijendra N. Pandey, Yuri N. Skiba   +2 more
wiley   +1 more source

Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces

Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013
We firstly deal with the existence of mild solutions for nonlocal fractional impulsive semilinear differential inclusions involving Caputo derivative in Banach spaces in the case when the linear part is the infinitesimal generator of a semigroup not necessarily compact. Meanwhile, we prove the compactness property of the set of solutions.
JinRong Wang, Ahmed G. Ibrahim, Henryk Hudzik   +2 more
wiley   +1 more source

Existence for Nonautonomous Fractional Integrodifferential Equations with Nonlocal Conditions

Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013
We study the existence of mild solution of a class of nonlinear nonautonomous fractional integrodifferential equations with nonlocal conditions in a separable Banach space X. Combining the techniques of operator semigroup, noncompactness measures, and the fixed point theory, we obtain new existence of mild solution without the assumptions that the ...
Fang Li, Dumitru Baleanu
wiley   +1 more source

Asymptotic behaviour of random tridiagonal Markov chains in biological applications

, 2012
Discrete-time discrete-state random Markov chains with a tridiagonal generator are shown to have a random attractor consisting of singleton subsets, essentially a random path, in the simplex of probability vectors.
A. E. Hutzenthaler, A. Leizarowitz, B. Noble, B. S. Thomson, D. J. Hartfiel, D. J. Hartfiel, D. N. Cheban, D. Wodarz, E. Asarin, H. Cohn, I. Chueshov, I. Chueshov, J. Wolfowitz, J.-P. Aubin, L. Arnold, L. J. S. Allen, M. A. Krasnosel$'$skij, M. F. Barnsley, M. Neumann, P. E. Kloeden, P. Imkeller, P. J. Bushell   +21 more
core   +1 more source