scholarly journals Boundary value problems of Hilfer-type fractional integro-differential equations and inclusions with nonlocal integro-multipoint boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1879-1894
Author(s):  
Cholticha Nuchpong ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Boundary Value ◽  
Case Examples ◽  
Uniqueness Results ◽  
Nonlinear Alternative ◽  
Differential Equations And Inclusions

Abstract In this paper, we study boundary value problems of fractional integro-differential equations and inclusions involving Hilfer fractional derivative. Existence and uniqueness results are obtained by using the classical fixed point theorems of Banach, Krasnosel’skiĭ, and Leray-Schauder in the single-valued case, while Martelli’s fixed point theorem, nonlinear alternative for multi-valued maps, and Covitz-Nadler fixed point theorem are used in the inclusion case. Examples illustrating the obtained results are also presented.

scholarly journals Nonlocal Sequential Boundary Value Problems for Hilfer Type Fractional Integro-Differential Equations and Inclusions

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 615
Author(s):  
Nawapol Phuangthong ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon ◽  
Kamsing Nonlaopon
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Boundary Value ◽  
Case Examples ◽  
Uniqueness Results ◽  
Nonlinear Alternative ◽  
Differential Equations And Inclusions

In the present research, we study boundary value problems for fractional integro-differential equations and inclusions involving the Hilfer fractional derivative. Existence and uniqueness results are obtained by using the classical fixed point theorems of Banach, Krasnosel’skiĭ, and Leray–Schauder in the single-valued case, while Martelli’s fixed point theorem, a nonlinear alternative for multivalued maps, and the Covitz–Nadler fixed point theorem are used in the inclusion case. Examples are presented to illustrate our results.

scholarly journals Three-Point Boundary Value Problems of Nonlinear Second-Orderq-Difference Equations Involving Different Numbers ofq

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Thanin Sitthiwirattham ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Difference Equations ◽  
Boundary Value ◽  
Point Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Uniqueness Results ◽  
Nonlinear Alternative

We study a new class of three-point boundary value problems of nonlinear second-orderq-difference equations. Our problems contain different numbers ofqin derivatives and integrals. By using a variety of fixed point theorems (such as Banach’s contraction principle, Boyd and Wong fixed point theorem for nonlinear contractions, Krasnoselskii’s fixed point theorem, and Leray-Schauder nonlinear alternative) and Leray-Schauder degree theory, some new existence and uniqueness results are obtained. Illustrative examples are also presented.

scholarly journals Boundary Value Problems for ψ-Hilfer Type Sequential Fractional Differential Equations and Inclusions with Integral Multi-Point Boundary Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1001
Author(s):  
Surang Sitho ◽  
Sotiris K. Ntouyas ◽  
Ayub Samadi ◽  
Jessada Tariboon
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Existence Result ◽  
Boundary Value ◽  
Point Boundary ◽  
Differential Equations And Inclusions

In the present article, we study a new class of sequential boundary value problems of fractional order differential equations and inclusions involving ψ-Hilfer fractional derivatives, supplemented with integral multi-point boundary conditions. The main results are obtained by employing tools from fixed point theory. Thus, in the single-valued case, the existence of a unique solution is proved by using the classical Banach fixed point theorem while an existence result is established via Krasnosel’skiĭ’s fixed point theorem. The Leray–Schauder nonlinear alternative for multi-valued maps is the basic tool to prove an existence result in the multi-valued case. Finally, our results are well illustrated by numerical examples.

scholarly journals Existence Results for Fractional Hahn Difference and Fractional Hahn Integral Boundary Value Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Nichaphat Patanarapeelert ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Hahn Integral

The existence and uniqueness results of two fractional Hahn difference boundary value problems are studied. The first problem is a Riemann-Liouville fractional Hahn difference boundary value problem for fractional Hahn integrodifference equations. The second is a fractional Hahn integral boundary value problem for Caputo fractional Hahn difference equations. The Banach fixed-point theorem and the Schauder fixed-point theorem are used as tools to prove the existence and uniqueness of solution of the problems.

scholarly journals On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay

2021 ◽  
Vol 26 (6) ◽  
pp. 1087-1105
Author(s):  
Yuxin Zhang ◽  
Xiping Liu ◽  
Mei Jia
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
State Variables ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence And Multiplicity

In this paper, we study the multi-point boundary value problems for a new kind of piecewise differential equations with left and right fractional derivatives and delay. In this system, the state variables satisfy the different equations in different time intervals, and they interact with each other through positive and negative delay. Some new results on the existence, no-existence and multiplicity for the positive solutions of the boundary value problems are obtained by using Guo–Krasnoselskii’s fixed point theorem and Leggett–Williams fixed point theorem. The results for existence highlight the influence of perturbation parameters. Finally, an example is given out to illustrate our main results.

Existence of solutions for Caputo fractional boundary value problems with integral conditions

2017 ◽  
Vol 33 (2) ◽  
pp. 207-217
Author(s):  
WENJUN LIU ◽  
◽  
HEFENG ZHUANG ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Boundary Value ◽  
Integral Conditions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Nonlinear Alternative ◽  
Banach’S Contraction Principle ◽  
Fractional Boundary Value Problems

In this paper, we investigate the existence results for Caputo fractional boundary value problems with integral conditions. Our analysis relies on Banach’s contraction principle, Leray-Schauder nonlinear alternative, Boyed and Wong fixed point theorem, and Krasnoselskii’s fixed point theorem. As applications, some examples are provided to illustrate our main results.

scholarly journals Existence criteria of positive solutions for fractional p-Laplacian boundary value problems

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3789-3799
Author(s):  
Deren Yoruk ◽  
Tugba Cerdik ◽  
Ravi Agarwal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Existence Of Positive Solutions ◽  
Existence Criteria

By means of the Bai-Ge?s fixed point theorem, this paper shows the existence of positive solutions for nonlinear fractional p-Laplacian differential equations. Here, the fractional derivative is the standard Riemann-Liouville one. Finally, an example is given to illustrate the importance of results obtained.

scholarly journals On the Nonhomogeneous Fourth-Orderp-Laplacian Generalized Sturm-Liouville Nonlocal Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jian Liu ◽  
Zengqin Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Fourth Order ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlinear Alternative ◽  
Sturm Liouville

We study the nonlinear nonhomogeneousn-point generalized Sturm-Liouville fourth-orderp-Laplacian boundary value problem by using Leray-Schauder nonlinear alternative and Leggett-Williams fixed-point theorem.

scholarly journals RETRACTED ARTICLE: Existence and uniqueness of solutions for the Schrödinger integrable boundary value problem

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Jianjie Wang ◽  
Ali Mai ◽  
Hong Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Of Solutions ◽  
Linear Maps ◽  
Retracted Article

Abstract This paper is mainly devoted to the study of one kind of nonlinear Schrödinger differential equations. Under the integrable boundary value condition, the existence and uniqueness of the solutions of this equation are discussed by using new Riesz representations of linear maps and the Schrödinger fixed point theorem.

scholarly journals Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space

2020 ◽  
Vol 19 (1) ◽  
pp. 171-192
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Mönch Fixed Point Theorem

AbstractIn this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss Eα -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution.

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