scholarly journals Investigation of the Fractional Strongly Singular Thermostat Model via Fixed Point Techniques

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2298
Author(s):  
Mohammed K. A. Kaabar ◽  
Mehdi Shabibi ◽  
Jehad Alzabut ◽  
Sina Etemad ◽  
Weerawat Sudsutad ◽  
...  
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Existence Of Solutions ◽  
Control Model ◽  
Generalized Boundary Conditions ◽  
Admissible Maps ◽  
The Given ◽  
Thermostat Model ◽  
Fixed Point Techniques

Our main purpose in this paper is to prove the existence of solutions for the fractional strongly singular thermostat model under some generalized boundary conditions. In this way, we use some recent nonlinear fixed-point techniques involving α-ψ-contractions and α-admissible maps. Further, we establish the similar results for the hybrid version of the given fractional strongly singular thermostat control model. Some examples are studied to illustrate the consistency of our results.

scholarly journals On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1205
Author(s):  
Usman Riaz ◽  
Akbar Zada ◽  
Zeeshan Ali ◽  
Ioan-Lucian Popa ◽  
Shahram Rezapour ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Coupled System ◽  
Initial Boundary ◽  
Liouville Type ◽  
Liouville Derivative ◽  
Banach Contraction ◽  
Generalized Boundary Conditions

We study a coupled system of implicit differential equations with fractional-order differential boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, and at least one solution are established by applying the Banach contraction and Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities are discussed. An example is presented to illustrate our main result. The suggested system is the generalization of fourth-order ordinary differential equations with anti-periodic, classical, and initial boundary conditions.

scholarly journals The Existence of Positive Solutions for Fractional Differential Equations with Sign Changing Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Weihua Jiang ◽  
Jiqing Qiu ◽  
Weiwei Guo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Eigenvalue Problems ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Generalized Boundary Conditions

We investigate the existence of at least two positive solutions to eigenvalue problems of fractional differential equations with sign changing nonlinearities in more generalized boundary conditions. Our analysis relies on the Avery-Peterson fixed point theorem in a cone. Some examples are given for the illustration of main results.

scholarly journals APPROXIMATE ENDPOINT SOLUTIONS FOR A CLASS OF FRACTIONAL q-DIFFERENTIAL INCLUSIONS BY COMPUTATIONAL RESULTS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040029 ◽  
Author(s):  
S. M. AYDOGAN ◽  
J. F. GÓMEZ AGUILAR ◽  
D. BALEANU ◽  
SH. REZAPOUR ◽  
M. E. SAMEI
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Numerical Results ◽  
Computational Results ◽  
Integral Boundary ◽  
Fixed Point Techniques

By using the notion of endpoints for set-valued functions and some classical fixed point techniques, we investigate the existence of solutions for two fractional [Formula: see text]-differential inclusions under some integral boundary value conditions. By providing an example, we illustrate our main result about endpoint. Also, we give some related algorithms and numerical results.

scholarly journals On a Generalized Langevin Type Nonlocal Fractional Integral Multivalued Problem

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1015 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Madeaha Alghanmi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Multivalued Map ◽  
Multivalued Maps ◽  
Nadler’S Fixed Point Theorem ◽  
Nonlinear Alternative ◽  
The Given ◽  
Fractional Order Integral

We establish sufficient criteria for the existence of solutions for a nonlinear generalized Langevin-type nonlocal fractional-order integral multivalued problem. The convex and non-convex cases for the multivalued map involved in the given problem are considered. Our results rely on Leray–Schauder nonlinear alternative for multivalued maps and Covitz and Nadler’s fixed point theorem. Illustrative examples for the main results are included.

scholarly journals An Existence Theorem for Fractional Hybrid Differential Inclusions of Hadamard Type with Dirichlet Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Dirichlet Boundary Conditions

This paper studies the existence of solutions for a boundary value problem of nonlinear fractional hybrid differential inclusions by using a fixed point theorem due to Dhage (2006). The main result is illustrated with the aid of an example.

scholarly journals ON EXISTENCE OF SOLUTIONS FOR NONLINEAR Q-DIFFERENCE EQUATIONS WITH NONLOCAL Q-INTEGRAL BOUNDARY CONDITIONS

2015 ◽  
Vol 20 (5) ◽  
pp. 604-618 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Guotao Wang ◽  
Bashir Ahmad ◽  
Lihong Zhang ◽  
Aatef Hobiny ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
The Given

In this paper, we discuss the existence of solutions for nonlinear qdifference equations with nonlocal q-integral boundary conditions. The first part of the paper deals with some existence and uniqueness results obtained by means of standard tools of fixed point theory. In the second part, sufficient conditions for the existence of extremal solutions for the given problem are established. The results are well illustrated with the aid of examples.

scholarly journals Some Results on Fractional m-Point Boundary Value Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Huijuan Zhu ◽  
Baozhi Han ◽  
Jun Shen
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Lyapunov’S Inequality ◽  
The Given ◽  
Stability Results

In this paper, we will apply some fixed-point theorems to discuss the existence of solutions for fractional m-point boundary value problems D 0 + q u ″ t = h t f u t , t ∈ 0 , 1 , 1 < q ≤ 2 , u ′ 0 = u ″ 0 = u 1 = 0 , u ″ 1 − ∑ i = 1 m − 2 α i u ‴ ξ i = 0 . In addition, we also present Lyapunov’s inequality and Ulam-Hyers stability results for the given m-point boundary value problems.

scholarly journals An Analytical Survey on the Solutions of the Generalized Double-Order φ -Integrodifferential Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Sh. Rezapour ◽  
S. K. Ntouyas ◽  
M. Q. Iqbal ◽  
A. Hussain ◽  
S. Etemad ◽  
...  
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Integrodifferential Equation ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
Banach Contraction Principle ◽  
Integral Boundary ◽  
Banach Contraction ◽  
The Banach Contraction Principle ◽  
Schauder Fixed Point

We study the existence of solutions for a newly configured model of a double-order integrodifferential equation including φ -Caputo double-order φ -integral boundary conditions. In this way, we use the Krasnoselskii and Leray-Schauder fixed point results. Also, we invoke the Banach contraction principle to confirm the uniqueness of the existing solutions. Finally, we provide three examples to illustrate our analytical findings.

The existence of axially symmetric flow above a rotating disk

1971 ◽  
Vol 324 (1559) ◽  
pp. 391-414 ◽  
Keyword(s):  
Fixed Point ◽  
Angular Velocity ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence Of Solutions ◽  
Rotating Disk ◽  
Fixed Point Method ◽  
Axially Symmetric ◽  
Symmetric Flow ◽  
Shooting Technique

The paper studies the boundary-value problem arising from the behaviour of a fluid occupying the half space x > 0 above a rotating disk which is coincident with the plane x = 0 and rotates about its axis which remains fixed. The equations which describe axially symmetric solutions of this problem are f ''' + ff ''+½( g 2 – f ' 2 ) = ½ Ω 2 ∞ , g "+ fg ' = f ' g , with the boundary conditions f (0) = a , f '(0) = 0, g (0) = Ω 0 ); f '(∞) = 0, g (∞) = Ω ∞ , where a is a constant measuring possible suction at the disk, Ω 0 is the angular velocity of the disk, and Ω ∞ is an angular velocity to which the fluid is subjected at infinity. When Ω ∞ = 0, existence of solutions has previously been proved by the ‘shooting technique’. This method breaks down when Ω 0 ǂ 0 because of oscillations in the functions f and g , but in the present paper existence is first proved by a fixed point method when Ω 0 is close to Ω ∞ and then extended for all Ω 0 , with the important restriction that Ω 0 and Ω ∞ be of the same sign.

scholarly journals Existence of Solutions for Some Nonlinear Problems with Boundary Value Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Dionicio Pastor Dallos Santos
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlinear Problems ◽  
Nonlinear Boundary Value Problems

We study the existence of solutions for nonlinear boundary value problemsφu′′=ft,u,u′,  lu,u′=0, wherel(u,u′)=0denotes the boundary conditions on a compact interval0,T,φis a homeomorphism such thatφ(0)=0, andf:0,T×R×R→Ris a continuous function. All the contemplated boundary value problems are reduced to finding a fixed point for one operator defined on a space of functions, and Schauder fixed point theorem or Leray-Schauder degree is used.

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