New Existence Results for Nonlinear Fractional Integrodifferential Equations

This paper discusses a boundary value problem of nonlinear fractional integrodifferential equations of order 1 < α ≤ 2 and 1 < β ≤ 2 and boundary conditions of the form x 0 = x 1 = D c β x 1 = D c β x 0 = 0 . Some new existence and uniqueness results are proposed by using the fixed point theory. In particular, we make use of the Banach contraction mapping principle and Krasnoselskii’s fixed point theorem under some weak conditions. Moreover, two illustrative examples are studied to support the results.

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On a Nonlocal Multipoint and Integral Boundary Value Problem of Nonlinear Fractional Integrodifferential Equations

Journal of Function Spaces ◽

10.1155/2020/8891736 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Lahcen Ibnelazyz ◽

Karim Guida ◽

Said Melliani ◽

Khalid Hilal

Keyword(s):

Fixed Point ◽

Boundary Value Problem ◽

Fixed Point Theory ◽

Boundary Value ◽

Point Theory ◽

Integrodifferential Equations ◽

Integral Boundary ◽

Krasnoselskii’S Fixed Point Theorem ◽

Integral Boundary Value Problem ◽

Uniqueness Results

The aim of this paper is to give the existence as well as the uniqueness results for a multipoint nonlocal integral boundary value problem of nonlinear sequential fractional integrodifferential equations. First of all, we give some preliminaries and notations that are necessary for the understanding of the manuscript; second of all, we show the existence and uniqueness of the solution by means of the fixed point theory, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Last, but not least, we give two examples to illustrate the results.

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Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2018074 ◽

2019 ◽

Vol 14 (3) ◽

pp. 311 ◽

Cited By ~ 39

Author(s):

Muhammad Altaf Khan ◽

Zakia Hammouch ◽

Dumitru Baleanu

Keyword(s):

Fixed Point ◽

Existence And Uniqueness ◽

Numerical Scheme ◽

Arbitrary Order ◽

Fixed Point Theory ◽

Hepatitis E ◽

Point Theory ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

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

Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica ◽

10.2478/aupcsm-2020-0013 ◽

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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Terminal Value Problem for Differential Equations with Hilfer–Katugampola Fractional Derivative

Symmetry ◽

10.3390/sym11050672 ◽

2019 ◽

Vol 11 (5) ◽

pp. 672 ◽

Cited By ~ 2

Author(s):

Mouffak Benchohra ◽

Soufyane Bouriah ◽

Juan J. Nieto

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Fractional Derivative ◽

Fixed Point Theory ◽

Point Theory ◽

Uniqueness Of Solutions ◽

Krasnoselskii’S Fixed Point Theorem ◽

Banach Contraction ◽

Fractional Differential ◽

Terminal Value Problem

We present in this work the existence results and uniqueness of solutions for a class of boundary value problems of terminal type for fractional differential equations with the Hilfer–Katugampola fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Banach contraction principle and Krasnoselskii’s fixed point theorem. We illustrate our main findings, with a particular case example included to show the applicability of our outcomes.

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Solvability for Discrete Fractional Boundary Value Problems with ap-Laplacian Operator

Discrete Dynamics in Nature and Society ◽

10.1155/2013/679290 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 3

Author(s):

Weidong Lv

Keyword(s):

Contraction Mapping ◽

Boundary Value ◽

Contraction Mapping Principle ◽

Laplacian Operator ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Banach Contraction ◽

Banach Contraction Mapping Principle ◽

Fractional Boundary Value Problems ◽

Banach Contraction Mapping

This paper is concerned with the solvability for a discrete fractionalp-Laplacian boundary value problem. Some existence and uniqueness results are obtained by means of the Banach contraction mapping principle. Additionally, two representative examples are presented to illustrate the effectiveness of the main results.

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Existence Results for a Class of Fractional Differential Equations with Periodic Boundary Value Conditions and with Delay

Abstract and Applied Analysis ◽

10.1155/2013/176180 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 3

Author(s):

Hadi Karami ◽

Azizollah Babakhani ◽

Dumitru Baleanu

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Existence And Uniqueness ◽

Main Tool ◽

Uniqueness Of Solution ◽

Krasnoselskii’S Fixed Point Theorem ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Banach Contraction ◽

Delay Differential

We discuss the existence and uniqueness of solution for two types of fractional order ordinary and delay differential equations. Fixed point theorems are the main tool used here to establish the existence and uniqueness results. First we use Banach contraction principle to prove the uniqueness of solution and then Krasnoselskii's fixed point theorem to show the existence of the solution under certain conditions in a Banach space.

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Existence Results for Nonlinear Multiorder Fractional Differential Equations with Integral and Antiperiodic Boundary Conditions

Journal of Applied Mathematics ◽

10.1155/2020/1212040 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

HuiChol Choi ◽

YongSim Sin ◽

KumSong Jong

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Contraction Mapping Principle ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Banach Contraction ◽

Caputo Fractional Differential Equations ◽

Fractional Differential

In this paper, we study the solvability of a class of nonlinear multiorder Caputo fractional differential equations with integral and antiperiodic boundary conditions. By using some fixed point theorems including the Banach contraction mapping principle and Schaefer’s fixed point theorem, we obtain new existence and uniqueness results for our given problem. Also, we give some examples to illustrate our main results.

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Existence Theory forq-Antiperiodic Boundary Value Problems of Sequentialq-Fractional Integrodifferential Equations

Abstract and Applied Analysis ◽

10.1155/2014/207547 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12 ◽

Cited By ~ 3

Author(s):

Ravi P. Agarwal ◽

Bashir Ahmad ◽

Ahmed Alsaedi ◽

Hana Al-Hutami

Keyword(s):

Fixed Point ◽

Fixed Point Theory ◽

Point Theory ◽

Integrodifferential Equations ◽

Existence Theory ◽

Uniqueness Of Solutions ◽

Krasnoselskii’S Fixed Point Theorem ◽

New Class ◽

Nonlinear Alternative ◽

Banach’S Contraction Principle

We discuss the existence and uniqueness of solutions for a new class of sequentialq-fractional integrodifferential equations withq-antiperiodic boundary conditions. Our results rely on the standard tools of fixed-point theory such as Krasnoselskii's fixed-point theorem, Leray-Schauder nonlinear alternative, and Banach's contraction principle. An illustrative example is also presented.

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Existence Results for Impulsive Fractional q-Difference Equation with Antiperiodic Boundary Conditions

Journal of Function Spaces ◽

10.1155/2018/3798342 ◽

2018 ◽

Vol 2018 ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

Mingyue Zuo ◽

Xinan Hao

Keyword(s):

Difference Equation ◽

Contraction Mapping ◽

Contraction Mapping Principle ◽

Existence Results ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Nonlinear Alternative ◽

Banach Contraction ◽

Banach Contraction Mapping Principle ◽

Banach Contraction Mapping

In this paper, we investigate the impulsive fractional q-difference equation with antiperiodic conditions. The existence and uniqueness results of solutions are established via the theorem of nonlinear alternative of Leray-Schauder type and the Banach contraction mapping principle. Two examples are given to illustrate our results.

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On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations

Mathematics ◽

10.3390/math8040476 ◽

2020 ◽

Vol 8 (4) ◽

pp. 476

Author(s):

Jiraporn Reunsumrit ◽

Thanin Sitthiwirattham

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Boundary Value Problem ◽

Boundary Conditions ◽

Difference Equations ◽

Existence And Uniqueness ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Banach Contraction ◽

The Banach Contraction Principle

In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example.

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