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 Existence results for fractional differential inclusions with Erdélyi-Kober fractional integral conditions

2017 ◽  
Vol 25 (2) ◽  
pp. 5-24 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Integral Conditions ◽  
Fractional Differential

Abstract In this paper, we discus the existence of solutions for Riemann- Liouville fractional differential inclusions supplemented with Erdélyi- Kober fractional integral conditions. We apply endpoint theory, Krasnoselskii’s multi-valued fixed point theorem and Wegrzyk's fixed point theorem for generalized contractions. For the illustration of our results, we include examples.

scholarly journals Existence of Positive Solution for the Eighth-Order Boundary Value Problem Using Classical Version of Leray–Schauder Alternative Fixed Point Theorem

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 129 ◽  
Author(s):  
Thenmozhi Shanmugam ◽  
Marudai Muthiah ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Eighth Order ◽  
Classical Version ◽  
Nonlinear Alternative

In this work, we investigate the existence of solutions for the particular type of the eighth-order boundary value problem. We prove our results using classical version of Leray–Schauder nonlinear alternative fixed point theorem. Also we produce a few examples to illustrate our results.

scholarly journals Existence of solutions of Sobolev-type semilinear mixed integrodifferential inclusions in Banach spaces

2003 ◽  
Vol 16 (2) ◽  
pp. 163-170 ◽  
Author(s):  
M. Kanakaraj ◽  
K. Balachandran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Topological Spaces ◽  
Sobolev Type ◽  
Multivalued Maps ◽  
Locally Convex

The existence of mild solutions of Sobolev-type semilinear mixed integrodifferential inclusions in Banach spaces is proved using a fixed point theorem for multivalued maps on locally convex topological spaces.

scholarly journals Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Jessada Tariboon ◽  
Sotiris K. Ntouyas ◽  
Chatthai Thaiprayoon
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Langevin Equation ◽  
Fractional Derivatives ◽  
Fractional Integral ◽  
Integral Conditions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Nonlinear Alternative ◽  
Nonlinear Langevin Equation

We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder’s degree theory. Enlightening examples illustrating the obtained results are also presented.

scholarly journals On the existence of solutions for Volterra integral inclusions in Banach spaces

1993 ◽  
Vol 6 (3) ◽  
pp. 261-269
Author(s):  
Evgenios P. Avgerinos
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Of Solutions ◽  
Existence Results ◽  
The Other ◽  
Multivalued Map ◽  
Volterra Type ◽  
The Right ◽  
Condensing Maps

In this paper we examine a class of nonlinear integral inclusions defined in a separable Banach space. For this class of inclusions of Volterra type we establish two existence results, one for inclusions with a convex-valued orientor field and the other for inclusions with nonconvex-valued orientor field. We present conditions guaranteeing that the multivalued map that represents the right-hand side of the inclusion is α-condensing using for the proof of our results a known fixed point theorem for α-condensing maps.

scholarly journals On a System of Volterra Type Hadamard Fractional Integral Equations in Fréchet Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Fréchet Spaces ◽  
Volterra Type ◽  
The Fixed Point Theorem ◽  
Hadamard Fractional Integral

In this article we present some results concerning the existence of solutions for a system of Hadamard integral equations. Our investigation is conducted with an application of an extension of the fixed point theorem of Burton-Kirk in Fréchet spaces.

scholarly journals Nonlocal Boundary Value Problems of Nonlinear Fractional (p,q)-Difference Equations

2021 ◽  
Vol 5 (4) ◽  
pp. 270
Author(s):  
Pheak Neang ◽  
Kamsing Nonlaopon ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equations ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Given

In this paper, we study nonlinear fractional (p,q)-difference equations equipped with separated nonlocal boundary conditions. The existence of solutions for the given problem is proven by applying Krasnoselskii’s fixed-point theorem and the Leray–Schauder alternative. In contrast, the uniqueness of the solutions is established by employing Banach’s contraction mapping principle. Examples illustrating the main results are also presented.

scholarly journals Existence of Solutions for Fractional-Order Neutral Differential Inclusions with Impulsive and Nonlocal Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Chao Song ◽  
Tao Zhu ◽  
Jinde Cao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Multivalued Maps ◽  
Impulsive Differential Inclusions ◽  
Theoretical Results

This paper investigates the existence of solutions for fractional-order neutral impulsive differential inclusions with nonlocal conditions. Utilizing the fractional calculus and fixed point theorem for multivalued maps, new sufficient conditions are derived for ensuring the existence of solutions. The obtained results improve and generalize some existed results. Finally, an illustrative example is given to show the effectiveness of theoretical results.

scholarly journals Multivalued impulsive neutral functional differential inclusions in Banach spaces

2002 ◽  
Vol 33 (1) ◽  
pp. 67-78
Author(s):  
M. Benchohra ◽  
J. Henderson ◽  
S. K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Semigroup Theory ◽  
Multivalued Maps ◽  
Functional Differential ◽  
Functional Differential Inclusions

In paper the existence of solutions for first and second order impulsive neutral functional differential inclusions in Banach spaces is investigated. The results are obtained by using a fixed point theorem for condensing multivalued maps due to Martelli and the semigroup theory.

Solvability of a 2 x 2 block operator matrix of chandrasekhar type on a Bananch algebra

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5169-5175 ◽  
Author(s):  
H.H.G. Hashem
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Of Solutions ◽  
Banach Algebras ◽  
Operator Matrix ◽  
Nonlinear Operators ◽  
Block Operator Matrix ◽  
Block Operator ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

In this paper, we study the existence of solutions for a system of quadratic integral equations of Chandrasekhar type by applying fixed point theorem of a 2 x 2 block operator matrix defined on a nonempty bounded closed convex subsets of Banach algebras where the entries are nonlinear operators.

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