scholarly journals On a class of differential inclusions in the frame of generalized Hilfer fractional derivative

2022 ◽  
Vol 7 (3) ◽  
pp. 3477-3493
Author(s):  
Adel Lachouri ◽  
◽  
Mohammed S. Abdo ◽  
Abdelouaheb Ardjouni ◽  
Bahaaeldin Abdalla ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fractional Derivative ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Hilfer Fractional Derivative ◽  
Integral Boundary ◽  
Inclusion Problems ◽  
Nonlocal Integral Boundary Conditions

<abstract><p>In the present paper, we extend and develop a qualitative analysis for a class of nonlinear fractional inclusion problems subjected to nonlocal integral boundary conditions (nonlocal IBC) under the $ \varphi $-Hilfer operator. Both claims of convex valued and nonconvex valued right-hand sides are investigated. The obtained existence results of the proposed problem are new in the frame of a $ \varphi $-Hilfer fractional derivative with nonlocal IBC, which are derived via the fixed point theorems (FPT's) for set-valued analysis. Eventually, we give some illustrative examples for the acquired results.</p></abstract>

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.

scholarly journals Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1905
Author(s):  
Athasit Wongcharoen ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Nonlocal Integral Boundary Conditions

In this paper, we study boundary value problems for differential inclusions, involving Hilfer fractional derivatives and nonlocal integral boundary conditions. New existence results are obtained by using standard fixed point theorems for multivalued analysis. Examples illustrating our results are also presented.

scholarly journals Hilfer fractional differential inclusions with Erdélyi–Kober fractional integral boundary condition

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adel Lachouri ◽  
Mohammed S. Abdo ◽  
Abdelouaheb Ardjouni ◽  
Bahaaeldin Abdalla ◽  
Thabet Abdeljawad
Keyword(s):  
Differential Inclusions ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
Fractional Differential Inclusions ◽  
Hilfer Fractional Derivative ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Theoretical Results

AbstractIn this article, we debate the existence of solutions for a nonlinear Hilfer fractional differential inclusion with nonlocal Erdélyi–Kober fractional integral boundary conditions (FIBC). Both cases of convex- and nonconvex-valued right-hand side are considered. Our obtained results are new in the framework of Hilfer fractional derivative and Erdélyi–Kober fractional integral with FIBC via the fixed point theorems (FPTs) for a set-valued analysis. Some pertinent examples demonstrating the effectiveness of the theoretical results are presented.

scholarly journals Existence Results for Fractional Differential Inclusions with Multivalued Term Depending on Lower-Order Derivative

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Xiaoyou Liu ◽  
Zhenhai Liu
Keyword(s):  
Boundary Conditions ◽  
Lower Order ◽  
Differential Inclusions ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Inclusion Problem ◽  
Fractional Differential Inclusions ◽  
Integral Boundary ◽  
Separated Boundary Conditions ◽  
Fractional Differential

This paper is concerned with a class of fractional differential inclusions whose multivalued term depends on lower-order fractional derivative with fractional (non)separated boundary conditions. The cases of convex-valued and non-convex-valued right-hand sides are considered. Some existence results are obtained by using standard fixed point theorems. A possible generalization for the inclusion problem with integral boundary conditions is also discussed. Examples are given to illustrate the results.

scholarly journals Existence Theory for th Order Nonlocal Integral Boundary Value Problems and Extension to Fractional Case

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas ◽  
Hamed H. Alsulami
Keyword(s):  
Differential Equations ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Existence Theory ◽  
Uniqueness Of Solutions ◽  
Order Problem ◽  
Integral Boundary ◽  
Integral Boundary Value Problems ◽  
Nonlocal Integral Boundary Conditions ◽  
Higher Order Problem

This paper is devoted to the study of the existence and uniqueness of solutions for th order differential equations with nonlocal integral boundary conditions. Our results are based on a variety of fixed point theorems. Some illustrative examples are discussed. We also discuss the Caputo type fractional analogue of the higher-order problem of ordinary differential equations.

scholarly journals On Periodic Fractional (p, q)-Integral Boundary Value Problems for Sequential Fractional (p, q)-Integrodifference Equations

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 264
Author(s):  
Jarunee Soontharanon ◽  
Thanin Sitthiwirattham
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Integral Boundary Condition ◽  
Integrodifference Equations ◽  
Integrodifference Equation ◽  
Integral Boundary ◽  
Integral Boundary Value Problems

We study the existence results of a fractional (p, q)-integrodifference equation with periodic fractional (p, q)-integral boundary condition by using Banach and Schauder’s fixed point theorems. Some properties of (p, q)-integral are also presented in this paper as a tool for our calculations.

scholarly journals Positive solutions for generalized two-term fractional differential equations with integral boundary conditions

2020 ◽  
Vol 1 (1) ◽  
pp. 47-63
Author(s):  
Hanan A. Wahash ◽  
Satish K. Panchal
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Upper And Lower Solutions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential

In this paper, we consider a class of boundary value problems for nonlinear two-term fractional differential equations with integral boundary conditions involving two $\psi $-Caputo fractional derivative. With the help of the properties Green function, the fixed point theorems of Schauder and Banach, and the method of upper and lower solutions, we derive the existence and uniqueness of positive solution of a proposed problem. Finally, an example is provided to illustrate the acquired results.

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