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Items from 1 to 20 out of 318 results

article

Pullback attractor for differential evolution inclusions with infinite delays

Nguyen Van Dac, Tran Dinh Ke, N. Van Dac, T. Dinh Ke

Applied Mathematics and Computation > 2015 > 265 > Complete > 667-680

We analyze the existence of pullback attractor for non-autonomous differential inclusions with infinite delays in Banach spaces by using measures of noncompactness. The obtained results can be applied to control systems driven by semilinear partial differential equations and multivalued feedbacks.

article

On the (k,Ψ)‐Hilfer nonlinear impulsive fractional differential equations

Jyoti P. Kharade, Kishor D. Kucche

Mathematical Methods in the Applied Sciences > 46 > 15 > 16282 - 16304

In this paper, the

(k, Ψ)

‐Hilfer fractional derivative, the most generalized fractional derivative operator, is used to analyze nonlinear impulsive fractional differential equations. The initial goal of this work is to provide a suitable representation formula for the solutions of the

(k, Ψ)

‐Hilfer nonlinear impulsive fractional differential equations...

article

On the solvability of a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator

Vijai Kumar Pathak, Lakshmi Narayan Mishra, Vishnu Narayan Mishra

Mathematical Methods in the Applied Sciences > 46 > 13 > 14340 - 14352

In this paper, utilizing the technique of generalized Darbo's fixed‐point theorem associated with measure of noncompactness in Banach space, we analyze the existence of solution for a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator. The existing result was obtained to strengthen the ones mentioned previously in the literature. An example for a class of...

article

Mild solutions of semilinear evolution equation and their applications in second‐order hyperbolic PDE

Mohammad Mursaleen, Asghar Allahyari, Hojjatollah Amiri Kayvanloo, Ali Shole Haghighi, more

Mathematical Methods in the Applied Sciences > 46 > 9 > 10719 - 10729

The principal goal of this work is to solvability of the mild solution for the second‐order hyperbolic PDE with initial/boundary‐value problem with nonlocal condition of the form where

P \subseteq ℝ^{n}

is open. Our analysis relies on the technique of measure of noncompactness.

article

Approximate controllability results in α-norm for some partial functional integrodifferential equations with nonlocal initial conditions in Banach spaces

Patrice Ndambomve, Moussa El-Khalil Kpoumie, Khalil Ezzinbi

Journal of Applied Analysis > 2023 > Vol. 29, nr 1 > 127--142

In this work, we discuss the approximate controllability of some nonlinear partial functional integrodifferential equations with nonlocal initial condition in Hilbert spaces.We assume that the corresponding linear part is approximately controllable. The results are obtained by using fractional power theory and α-norm, the measure of noncompactness and theMönch fixed-point theorem, and the theory of...

article

Almost sectorial operators on Ψ‐Hilfer derivative fractional impulsive integro‐differential equations

Kulandhivel Karthikeyan, Panjaiyan Karthikeyan, Haci Mehmet Baskonus, Kuppusamy Venkatachalam, more

Mathematical Methods in the Applied Sciences > 45 > 13 > 8045 - 8059

This paper is concerned with the existence results of Ψ‐Hilfer fractional impulsive integro‐differential equations involving almost sectorial operators. The mild solutions of the problems are proved by using Schauder fixed‐point theorem along with measure of noncompactness. We have discussed the two cases of operators associated semigroup. Also, we consider an abstract application via Hilfer fractional...

article

Analyzing the existence of solution of a fractional order integral equation: A fixed point approach

Dipankar Saha, Mausumi Sen, Santanu Roy

Journal of Applied Analysis > 2022 > Vol. 28, nr 2 > 199--210

This paper signifies the beauty of fixed point theory in the context of attaining the sufficient condition for the existence of the solution of a non-linear functional-integral equation in an unbounded interval. Here a non-linear integral equation (NLIE) involving a fractional operator is taken in the form of an operator equation. Utilizing the perception of measure of noncompactness (MNC) along with...

article

On the hybrid Caputo-proportional fractional differential inclusions in Banach spaces

Mohamed I. Abbas

Journal of Mathematics and Applications > 2022 > Vol. 45 > 5--20

The current article concerns an existence criteria of solutions of nonlinear fractional differential inclusions in the sense of the hybrid Caputo-proportional fractional derivatives in Banach space. The investigation of the main result relies on the set-valued issue of Mönch fixed point theorem incorporated with the Kuratowski measure of non-compactness.

article

Controllability of multi-term time-fractional differential systems with state-dependent delay

Renu Chaudhary, Vikram Singh, D. N. Pandey

Journal of Applied Analysis > 2020 > Vol. 26, nr 2 > 241--255

In this paper, controllability results for a class of multi-term time-fractional differential systems with state-dependent delay have been studied. The concept of fractional calculus, measure of noncompactness and Mönch fixed-point theorem has been implemented to obtain a new set of controllability results. Finally, an application is given to illustrate the obtained results.

article

A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay

V. Vijayakumar, R. Udhayakumar

Numerical Methods for Partial Differential Equations > 37 > 1 > 750 - 766

This article is primarily focusing on the existence of Sobolev‐type Hilfer fractional neutral integro‐differential systems via measure of noncompactness. We study our primary outcomes by employing fractional calculus, measure of noncompactness and fixed point technique. First, we discuss the existence of mild solution for the fractional evolution system. Then, we extend our results to discuss the...

article

Essential norm estimates for multilinear singular and fractional integrals

Alexander Meskhi

Commentationes Mathematicae > 2019 > Vol. 59, No. 1/2 > 81--93

We derive lower two-weight estimates for the essential norm (measure of noncompactness) for multilinear Hilbert and Riesz transforms, and Riesz potential operators in Banach function lattices. As a corollary we have appropriate results in weighted Lebesgue spaces. From these statements we conclude that there is no (m + 1)-tuple of weights (v, w₁, w_m) for which these operators are compact from L_w1^p1...

article

On the Boundary Value Problem for Functional Differential Inclusion of Fractional Order with General Initial Condition in a Banach Space

M. S. Afanasova, G. G. Petrosyan

Russian Mathematics > 2019 > 63 > 9 > 1-11

We consider the problem for a functional differential inclusion of fractional order with a general initial condition expressed in the form of an operator inclusion in a Banach space. At the beginning of the paper, an introduction is presented in which the relevance of the study is substantiated, then preliminary information from fractional analysis, the theory of measures of noncompactness and condensing...

article

Existence Results of Damped Second Order Impulsive Functional Differential Equations with Infinite Delay

Sheng-li Xie, Yi-ming Xie

Acta Mathematicae Applicatae Sinica, English Series > 2019 > 35 > 3 > 564-579

Using the Mönch fixed point theorem and progressive estimation method, we study the existence, uniqueness and regularity of mild solutions for damped second order impulsive functional differential equations with infinite delay in Banach spaces. The compactness assumption on associated family of operators and the impulsive term, some restrictive conditions on a priori estimation, noncompactness measure...

article

PC-Mild Solutions to Sobolev-Type Fractional Differential Equations with Non-instantaneous Impulses

Vikram Singh, Dwijendra N. Pandey

Mediterranean Journal of Mathematics > 2019 > 16 > 4 > 1-20

In this paper, we study the existence and uniqueness of piecewise-continuous (in brief, PC)-mild solutions for Sobolev-type fractional impulsive differential equations (in brief, STFIDEs) with state-dependent delay by virtue of Kuratowski measure of noncompactness in a Banach space. We establish a general framework to find PC-mild solutions for STFIDEs with compact and noncompact semigroups, which...

article

Applications of Measure of Noncompactness and Operator Type Contraction for Existence of Solution of Functional Integral Equations

Bipan Hazarika, Reza Arab, M. Mursaleen

Complex Analysis and Operator Theory > 2019 > 13 > 8 > 3837-3851

The objective of this paper is to study the existence of solution of functional integral equations using a measure of noncompactness argument combined with generalized coupled fixed point theorem with the help of operator type contraction mapping in Banach spaces. We present an example to illustrate our results.

article

Solvability of infinite systems of third-order differential equations in $$c_{0}$$ c0 by Meir–Keeler condensing operators

R. Saadati, E. Pourhadi, M. Mursaleen

Journal of Fixed Point Theory and Applications > 2019 > 21 > 2 > 1-16

Throughout this work, using the technique of measure of noncompactness together with Meir–Keeler condensing operators, we study the solvability of the following infinite system of third-order differential equations in the Banach sequence space $$c_0 $$ c0 as a closed subspace of $$ \ell ^{\infty } $$ ℓ∞ : $$\begin{aligned} u_{i}^{\prime \prime \prime }+au_{i}^{\prime \prime }+bu_{i}^{\prime }+cu_{i}...

article

A New Approach to the Generalization of Darbo’s Fixed Point Problem by Using Simulation Functions with Application to Integral Equations

Mehdi Asadi, Moosa Gabeleh, Calogero Vetro

Results in Mathematics > 2019 > 74 > 2 > 1-15

We investigate the existence of fixed points of self-mappings via simulation functions and measure of noncompactness. We use different classes of additional functions to get some general contractive inequalities. As an application of our main conclusions, we survey the existence of a solution for a class of integral equations under some new conditions. An example will be given to support our results.

article

Controllability of second‐order Sobolev‐type impulsive delay differential systems

Vikram Singh, Dwijendra N. Pandey

Mathematical Methods in the Applied Sciences > 42 > 5 > 1377 - 1388

In this paper, we study some controllability results for second‐order Sobolev‐type impulsive integrodifferential systems with finite delay. The results are obtained by using the concepts of measure of noncompactness and Mönch's fixed point theorem. Particularly, we consider the damping term y′(·) and find a control u such that the mild solution satisfies y(T) = y_T and

y^{'} (T) = y_{T}^{'}

. Finally, an application...

article

On the PC $\mathcal{PC}$-mild solutions of abstract fractional evolution equations with non-instantaneous impulses via the measure of noncompactness

R. Saadati, E. Pourhadi, B. Samet

Boundary Value Problems > 2019 > 2019 > 1 > 1-23

In this paper, we deal with the existence results for mild solutions of abstract fractional evolution equations with non-instantaneous impulses on an unbounded interval. We also establish the existence of S $\mathcal{S}$-asymptotically ω-periodic mild solutions. The applied techniques are supported by the concept of measure of noncompactness in conjunction with the well-known Darbo–Sadovskii and...

article

Existence and approximation of solutions to nonlocal boundary value problems for fractional differential inclusions

M. Kamenskii, V. Obukhovskii, G. Petrosyan, Jen-Chih Yao

Fixed Point Theory and Applications > 2019 > 2019 > 1 > 1-21

We study a semilinear fractional order differential inclusion in a separable Banach space E of the form DqCx(t)∈Ax(t)+F(t,x(t)),t∈[0,T], $$ {}^{C}D^{q}x(t)\in Ax(t)+ F\bigl(t,x(t)\bigr),\quad t\in [0,T], $$ where DqC ${}^{C}D^{q}$ is the Caputo fractional derivative of order 0<q<1 $0 < q < 1$, A:D(A)⊂E→E $A \colon D(A) \subset E \rightarrow E$ is a generator of a C0 $C_{0}$-semigroup,...

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Pullback attractor for differential evolution inclusions with infinite delays

On the (k,Ψ)‐Hilfer nonlinear impulsive fractional differential equations

On the solvability of a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator

Mild solutions of semilinear evolution equation and their applications in second‐order hyperbolic PDE

Approximate controllability results in α-norm for some partial functional integrodifferential equations with nonlocal initial conditions in Banach spaces

Almost sectorial operators on Ψ‐Hilfer derivative fractional impulsive integro‐differential equations

Analyzing the existence of solution of a fractional order integral equation: A fixed point approach

On the hybrid Caputo-proportional fractional differential inclusions in Banach spaces

Controllability of multi-term time-fractional differential systems with state-dependent delay

A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay

Essential norm estimates for multilinear singular and fractional integrals

On the Boundary Value Problem for Functional Differential Inclusion of Fractional Order with General Initial Condition in a Banach Space

Existence Results of Damped Second Order Impulsive Functional Differential Equations with Infinite Delay

PC-Mild Solutions to Sobolev-Type Fractional Differential Equations with Non-instantaneous Impulses

Applications of Measure of Noncompactness and Operator Type Contraction for Existence of Solution of Functional Integral Equations

Solvability of infinite systems of third-order differential equations in $$c_{0}$$ c0 by Meir–Keeler condensing operators

A New Approach to the Generalization of Darbo’s Fixed Point Problem by Using Simulation Functions with Application to Integral Equations

Controllability of second‐order Sobolev‐type impulsive delay differential systems

On the PC $\mathcal{PC}$-mild solutions of abstract fractional evolution equations with non-instantaneous impulses via the measure of noncompactness

Existence and approximation of solutions to nonlocal boundary value problems for fractional differential inclusions

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