scholarly journals Boundary value problems of nonlinear fractional q-difference (integral) equations with two fractional orders and four-point nonlocal integral boundary conditions

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1719-1736 ◽  
Author(s):  
Bashir Ahmad ◽  
Juan Nieto ◽  
Ahmed Alsaedi ◽  
Hana Al-Hutami
Keyword(s):  
Boundary Conditions ◽  
Integral Equations ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Existence Results ◽  
Integral Boundary ◽  
Nonlocal Integral Boundary Conditions ◽  
Fractional Orders

This paper investigates the existence of solutions for nonlinear fractional q-difference equations and q-difference integral equations involving two fractional orders with four-point nonlocal integral boundary conditions. The existence results are obtained by applying some traditional tools of fixed point theory, and are illustrated with examples.

scholarly journals Existence Results for a Riemann-Liouville-Type Fractional Multivalued Problem with Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hamed H. Alsulami ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Boundary Conditions ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Multivalued Maps ◽  
Liouville Type ◽  
Integral Boundary ◽  
Fractional Differential ◽  
The Right

We discuss the existence of solutions for a boundary value problem of Riemann-Liouville fractional differential inclusions of orderα∈(2,3]with integral boundary conditions. We establish our results by applying the standard tools of fixed point theory for multivalued maps when the right-hand side of the inclusion has convex as well as nonconvex values. An illustrative example is also presented.

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 Existence Results for Boundary Value Problems of Differential Inclusions with Three-Point Integral Boundary Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas ◽  
Ahmed Alsaedi
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Multivalued Maps ◽  
Integral Boundary ◽  
Nonlinear Alternative

We discuss the existence of solutions for a boundary value problem of second-order differential inclusions with three-point integral boundary conditions involving convex and nonconvex multivalued maps. Our results are based on the nonlinear alternative of Leray-Schauder type and some suitable theorems of fixed point theory.

scholarly journals Existence of solutions or nonlinear nth-order differential equations and inclusions with nonlocal and integral boundary conditions via fixed point theory

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2149-2162 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris Ntouyas ◽  
Hamed Alsulami
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Differential Equations And Inclusions

In this paper, a class of boundary value problems of nonlinear nth-order differential equations and inclusions with nonlocal and integral boundary conditions is studied. New existence results are obtained by means of some fixed point theorems. Examples are given for the illustration of the results.

scholarly journals Some remarks on a fractional integro-differential inclusion with boundary conditions

2015 ◽  
Vol 23 (1) ◽  
pp. 73-82
Author(s):  
Aurelian Cernea
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusion ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Filippov Type

AbstractWe study the existence of solutions for fractional integrodifferential inclusions of order q ∈ (1, 2] swith families of mixed, closed, strip and integral boundary conditions. We establish Filippov type existence results in the case of nonconvex set-valued maps.

scholarly journals The Existence Results of Solutions for System of Fractional Differential Equations with Integral Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Dongxia Zan ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Initial Point ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Fractional Differential

In this paper, we investigated the system of fractional differential equations with integral boundary conditions. By using a fixed point theorem in the Banach spaces, we get the existence of solutions for the fractional differential system. By constructing iterative sequences for any given initial point in space, we can approximate this solution. As an application, an example is presented to illustrate our main results.

scholarly journals A Study of Nonlinear Fractionalq-Difference Equations with Nonlocal Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Hana Al-Hutami
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Nonlocal Integral Boundary Conditions

This paper is concerned with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractionalq-difference equations with nonlocal integral boundary conditions. The existence results are obtained by applying some well-known fixed point theorems and illustrated with examples.

Caputo type fractional differential equations with nonlocal Riemann-Liouville and Erdélyi-Kober type integral boundary conditions

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4515-4529 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris Ntouyas ◽  
Jessada Tariboon ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

In this paper, we study nonlocal boundary value problems of nonlinear Caputo fractional differential equations supplemented with different combinations of Riemann-Liouville and Erd?lyi-Kober type fractional integral boundary conditions. By applying a variety of tools of fixed point theory, the desired existence and uniqueness results are obtained. Examples illustrating the main results are also constructed.

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