scholarly journals Compact and Noncompact Solutions to Generalized Sturm–Liouville and Langevin Equation with Caputo–Hadamard Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Ahmed Salem ◽  
Noorah Mshary ◽  
Moustafa El-Shahed ◽  
Faris Alzahrani
Keyword(s):  
Fractional Derivative ◽  
Fixed Point Theorems ◽  
Nonlinear Boundary ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Hadamard Fractional Derivative ◽  
Compact Case ◽  
New Type ◽  
Sturm Liouville ◽  
Hadamard Fractional Integral

In this work, through using the Caputo–Hadamard fractional derivative operator with three nonlocal Hadamard fractional integral boundary conditions, a new type of the fractional-order Sturm–Liouville and Langevin problem is introduced. The existence of solutions for this nonlinear boundary value problem is theoretically investigated based on the Krasnoselskii in the compact case and Darbo fixed point theorems in the noncompact case with aiding the Kuratowski’s measure of noncompactness. To demonstrate the applicability and validity of the main gained findings, some numerical examples are included.

scholarly journals Lyapunov-type inequalities for differential equation with Caputo–Hadamard fractional derivative under multipoint boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Youyu Wang ◽  
Yuhan Wu ◽  
Zheng Cao
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Hadamard Fractional Derivative ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Fractional Boundary Value Problems

AbstractIn this work, we establish Lyapunov-type inequalities for the fractional boundary value problems with Caputo–Hadamard fractional derivative subject to multipoint and integral boundary conditions. As far as we know, there is no literature that has studied these problems.

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 Non-Instantaneous Impulsive Boundary Value Problems Containing Caputo Fractional Derivative of a Function with Respect to Another Function and Riemann–Stieltjes Fractional Integral Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 130
Author(s):  
Suphawat Asawasamrit ◽  
Yasintorn Thadang ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Caputo Fractional Derivative ◽  
Fractional Integral ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Nonlinear Alternative

In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses and Caputo fractional derivative of a function with respect to another function, supplemented with Riemann–Stieltjes fractional integral boundary conditions. The existence of a unique solution is obtained via Banach’s contraction mapping principle, while an existence result is established by using Leray–Schauder nonlinear alternative. Examples illustrating the main results are also constructed.

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 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 Boundary Value Problems of Fractional Order Differential Equation with Integral Boundary Conditions and Not Instantaneous Impulses

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Peiluan Li ◽  
Changjin Xu
Keyword(s):  
Boundary Conditions ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Order Differential Equation ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Fractional Order Differential Equation ◽  
Uniqueness Of Solutions ◽  
Integral Boundary

We investigate the existence of mild solutions for fractional order differential equations with integral boundary conditions and not instantaneous impulses. By some fixed-point theorems, we establish sufficient conditions for the existence and uniqueness of solutions. Finally, two interesting examples are given to illustrate our theory results.

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