scholarly journals Application of some special operators on the analysis of a new generalized fractional Navier problem in the context of q-calculus

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sina Etemad ◽  
Sotiris K. Ntouyas ◽  
Atika Imran ◽  
Azhar Hussain ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fourth Order ◽  
Existence Of Solutions ◽  
Elastic Beam ◽  
Quantum Calculus ◽  
Multivalued Operators ◽  
Fractional Models ◽  
Navier Equation ◽  
Existence Criteria

AbstractThe key objective of this study is determining several existence criteria for the sequential generalized fractional models of an elastic beam, fourth-order Navier equation in the context of quantum calculus (q-calculus). The required way to accomplish the desired goal is that we first explore an integral equation of fractional order w.r.t. q-RL-integrals. Then, for the existence of solutions, we utilize some fixed point and endpoint conditions with the aid of some new special operators belonging to operator subclasses, orbital α-admissible and α-ψ-contractive operators and multivalued operators involving approximate endpoint criteria, which are constructed by using aforementioned integral equation. Furthermore, we design two examples to numerically analyze our results.

scholarly journals Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mahmoud Bousselsal ◽  
Sidi Hamidou Jah
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

On solutions of a stochastic integral equation of the volterra type with applications for chemotherapy

1988 ◽  
Vol 25 (02) ◽  
pp. 257-267 ◽  
Author(s):  
D. Szynal ◽  
S. Wedrychowicz
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Stochastic Model ◽  
Asymptotic Behaviour ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Volterra Type ◽  
Stochastic Integral Equation

This paper deals with the existence of solutions of a stochastic integral equation of the Volterra type and their asymptotic behaviour. Investigations of this paper use the concept of a measure of non-compactness in Banach space and fixed-point theorem of Darbo type. An application to a stochastic model for chemotherapy is also presented.

scholarly journals On a Fourth-Order Boundary Value Problem at Resonance

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Man Xu ◽  
Ruyun Ma
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Elastic Beam ◽  
First Eigenvalue ◽  
At Resonance ◽  
Problem At Resonance ◽  
Spectrum Structure

We investigate the spectrum structure of the eigenvalue problem u4x=λux,  x∈0,1;  u0=u1=u′0=u′1=0. As for the application of the spectrum structure, we show the existence of solutions of the fourth-order boundary value problem at resonance -u4x+λ1ux+gx,ux=hx,  x∈0,1;  u0=u1=u′0=u′1=0, which models a statically elastic beam with both end-points being cantilevered or fixed, where λ1 is the first eigenvalue of the corresponding eigenvalue problem and nonlinearity g may be unbounded.

scholarly journals An Extension of Darbo’s Theorem and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
A. Samadi ◽  
M. B. Ghaemi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Measures Of Noncompactness ◽  
Darbo Fixed Point Theorem ◽  
Real Functions

Here, some extensions of Darbo fixed point theorem associated with measures of noncompactness are proved. Then, as an application, our attention is focused on the existence of solutions of the integral equationx(t)=F(t,f(t,x(α1(t)),  x(α2(t))),((Tx)(t)/Γ(α))×∫0t‍(u(t,s,max⁡[0,r(s)]⁡|x(γ1(τ))|,  max⁡[0,r(s)]⁡|x(γ2(τ))|)/(t-s)1-α)ds,  ∫0∞v(t,s,x(t))ds),    0<α≤1,t∈[0,1]in the space of real functions defined and continuous on the interval[0,1].

scholarly journals On a nonlocal Cauchy problem for differential inclusions

2004 ◽  
Vol 2004 (5) ◽  
pp. 425-434 ◽  
Author(s):  
E. Gatsori ◽  
S. K. Ntouyas ◽  
Y. G. Sficas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Lower Semicontinuous ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Multivalued Operators ◽  
Nonlocal Cauchy Problem

We establish sufficient conditions for the existence of solutions for semilinear differential inclusions, with nonlocal conditions. We rely on a fixed-point theorem for contraction multivalued maps due to Covitz and Nadler andon the Schaefer's fixed-point theorem combined with lower semicontinuous multivalued operators with decomposable values.

scholarly journals A NONLINEAR F-CONTRACTION FORM OF SADOVSKII'S FIXED POINT THEOREM AND ITS APPLICATION TO A FUNCTIONAL INTEGRAL EQUATION OF VOLTERRA TYPE

2021 ◽  
pp. 321
Author(s):  
Kourosh Nourouzi ◽  
Faezeh Zahedi ◽  
Donal O'Regan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Volterra Type

In this paper, we give a nonlinear F-contraction form of the Sadovskii fixedpoint theorem and we also investigate the existence of solutions for a functional integral equation of Volterra type.

scholarly journals On a fractional cantilever beam model in the q-difference inclusion settings via special multi-valued operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sina Etemad ◽  
Azhar Hussain ◽  
Atika Imran ◽  
Jehad Alzabut ◽  
Shahram Rezapour ◽  
...  
Keyword(s):  
Integral Equation ◽  
Cantilever Beam ◽  
Fractional Integral ◽  
Existence Theory ◽  
Beam Model ◽  
Quantum Calculus ◽  
Fundamental Goal ◽  
Fractional Integral Equation ◽  
Existence Criteria ◽  
Difference Inclusion

AbstractThe fundamental goal of the study under consideration is to establish some of the existence criteria needed for a particular fractional inclusion model of cantilever beam in the setting of quantum calculus using new arguments of existence theory. In this way, we investigate a fractional integral equation that corresponds to the aforementioned boundary value problem. In a more concrete sense, we design new multi-valued operators based on this integral equation, which belong to the certain subclasses of functions, called α-admissible and α-ψ-contractive multi-functions, in combination with the AEP-property. Also, we use some inequalities such as Ω-inequality and set-valued version inequalities. Moreover, we add a simulative example for a numerical analysis of our results obtained in this study.

scholarly journals Krasnosel’skii Type Fixed Point Theorems for Mappings on Nonconvex Sets

2012 ◽  
Vol 2012 ◽  
pp. 1-23
Author(s):  
Maryam A. Alghamdi ◽  
Donal O'Regan ◽  
Naseer Shahzad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Normed Spaces ◽  
Nonconvex Sets

We prove Krasnosel'skii type fixed point theorems in situations where the domain is not necessarily convex. As an application, the existence of solutions for perturbed integral equation is considered inp-normed spaces.

scholarly journals The Existence of Symmetric Positive Solutions of Fourth-Order Elastic Beam Equations

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 121 ◽  
Author(s):  
Münevver Tuz
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Fourth Order ◽  
Eigenvalue Problems ◽  
Fixed Point Theory ◽  
Elastic Beam ◽  
Point Theory ◽  
Beam Equations ◽  
Symmetric Positive Solutions ◽  
Elastic Beam Equations

In this study, we consider the eigenvalue problems of fourth-order elastic beam equations. By using Avery and Peterson’s fixed point theory, we prove the existence of symmetric positive solutions for four-point boundary value problem (BVP). After this, we show that there is at least one positive solution by applying the fixed point theorem of Guo-Krasnosel’skii.

scholarly journals Existence of solutions of a class of stochastic Volterra integral equations with applications to chemotherapy

1999 ◽  
Vol 41 (1) ◽  
pp. 93-104 ◽  
Author(s):  
R. Subramaniam ◽  
K. Balachandran
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Stochastic Model ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Volterra Type ◽  
Stochastic Integral Equation ◽  
The Fixed Point Theorem

AbstractIn this paper we establish the existence of solutions of a more general class of stochastic integral equation of Volterra type. The main tools used here are the measure of noncompactness and the fixed point theorem of Darbo. The results generalize the results of Tsokos and Padgett [9] and Szynal and Wedrychowicz [7]. An application to a stochastic model arising in chemotherapy is discussed.

Sign in / Sign up

Export Citation Format

Share Document