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

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 and Uniqueness of Solutions for Coupled Impulsive Fractional Pantograph Differential Equations with Antiperiodic Boundary Conditions

Advances in Mathematical Physics ◽

10.1155/2021/6616899 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Karim Guida ◽

Lahcen Ibnelazyz ◽

Khalid Hilal ◽

Said Melliani

Keyword(s):

Differential Equation ◽

Fixed Point ◽

Differential Equations ◽

Existence And Uniqueness ◽

Uniqueness Of Solutions ◽

Krasnoselskii’S Fixed Point Theorem ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Fractional Differential ◽

Banach’S Contraction Principle

In this paper, we investigate the solutions of coupled fractional pantograph differential equations with instantaneous impulses. The work improves some existing results and contributes toward the development of the fractional differential equation theory. We first provide some definitions that will be used throughout the paper; after that, we give the existence and uniqueness results that are based on Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Two examples are given in the last part to support our study.

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EXISTENCE, UNIQUENESS AND STABILITY SOLUTIONS FOR NEW NONLINEAR SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS OF VOLTERRA TYPE

E-Jurnal Matematika ◽

10.24843/mtk.2020.v09.i02.p287 ◽

2020 ◽

Vol 9 (2) ◽

pp. 109

Author(s):

FARAJ YACOOB ISHAK

Keyword(s):

Fixed Point ◽

Nonlinear System ◽

Differential Equations ◽

Approximation Method ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Main Tool ◽

Volterra Type ◽

Existence And Uniqueness Results ◽

Uniqueness Results

In this article, we established the existence, uniqueness and stability solutions for a nonlinear system of integro-differential equations of Volterra type in Banach spaces. Krasnoselskii Fixed point theorems and Picard approximation method are the main tool used here to establish the existence and uniqueness results. A simple example of application of the main result of this paper is presented.

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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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On Caputo–Riemann–Liouville Type Fractional Integro-Differential Equations with Multi-Point Sub-Strip Boundary Conditions

Mathematics ◽

10.3390/math8111899 ◽

2020 ◽

Vol 8 (11) ◽

pp. 1899

Author(s):

Ahmed Alsaedi ◽

Amjad F. Albideewi ◽

Sotiris K. Ntouyas ◽

Bashir Ahmad

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Boundary Value Problem ◽

Boundary Conditions ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Boundary Value ◽

Liouville Type ◽

Existence And Uniqueness Results ◽

Uniqueness Results

In this paper, we derive existence and uniqueness results for a nonlinear Caputo–Riemann–Liouville type fractional integro-differential boundary value problem with multi-point sub-strip boundary conditions, via Banach and Krasnosel’skii⏝’s fixed point theorems. Examples are included for the illustration of the obtained results.

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Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations

Abstract and Applied Analysis ◽

10.1155/2012/632681 ◽

2012 ◽

Vol 2012 ◽

pp. 1-14 ◽

Cited By ~ 2

Author(s):

Azizollah Babakhani ◽

Dumitru Baleanu

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Fractional Order ◽

Existence And Uniqueness ◽

Initial Conditions ◽

Uniqueness Of Solution ◽

Fractional Order Differential Equations ◽

Banach Contraction ◽

Uniqueness Of The Solution

We discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations(Dα-ρtDβ)x(t)=f(t,x(t),Dγx(t)),t∈(0,1)with boundary conditionsx(0)=x0, x(1)=x1or satisfying the initial conditionsx(0)=0, x′(0)=1, whereDαdenotes Caputo fractional derivative,ρis constant,1<α<2,and0<β+γ≤α. Schauder's fixed-point theorem was used to establish the existence of the solution. Banach contraction principle was used to show the uniqueness of the solution under certain conditions onf.

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On Separate Fractional Sum-Difference Equations with n-Point Fractional Sum-Difference Boundary Conditions via Arbitrary Different Fractional Orders

Mathematics ◽

10.3390/math7050471 ◽

2019 ◽

Vol 7 (5) ◽

pp. 471 ◽

Cited By ~ 3

Author(s):

Saowaluck Chasreechai ◽

Thanin Sitthiwirattham

Keyword(s):

Fixed Point ◽

Boundary Conditions ◽

Existence And Uniqueness ◽

Nonlinear Functions ◽

Fractional Difference ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Banach Contraction ◽

Fractional Orders ◽

The Banach Contraction Principle

In this article, we study the existence and uniqueness results for a separate nonlinear Caputo fractional sum-difference equation with fractional difference boundary conditions by using the Banach contraction principle and the Schauder’s fixed point theorem. Our problem contains two nonlinear functions involving fractional difference and fractional sum. Moreover, our problem contains different orders in n + 1 fractional differences and m + 1 fractional sums. Finally, we present an illustrative example.

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Existence and Uniqueness Results for Two-Term Nonlinear Fractional Differential Equations via a Fixed Point Technique

Journal of Mathematics ◽

10.1155/2021/6670176 ◽

2021 ◽

Vol 2021 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

H. R. Marasi ◽

H. Aydi

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Monotone Operators ◽

Nonlinear Fractional Differential Equations ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Wide Range ◽

Fractional Differential

The work addressed in this paper is to ensure the existence and uniqueness of positive solutions for initial value problems for nonlinear fractional differential equations with two terms of fractional orders. By virtue of recent fixed point theorems on mixed monotone operators, we get some new straightforward results with a wide range of applications.

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Existence and uniqueness results for a class of BVPs for nonlinear fractional differential equations

Georgian Mathematical Journal ◽

10.1515/gmj-2014-0054 ◽

2015 ◽

Vol 22 (1) ◽

Cited By ~ 2

Author(s):

Djamal Foukrach ◽

Toufik Moussaoui ◽

Sotiris K. Ntouyas

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Boundary Value Problems ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Nonlinear Fractional Differential Equations ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Fractional Differential

AbstractThis paper studies some new existence and uniqueness results for boundary value problems for nonlinear fractional differential equations by using a variety of fixed point theorems. Some illustrative examples are also presented.

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New Existence Results for Nonlinear Fractional Integrodifferential Equations

Advances in Mathematical Physics ◽

10.1155/2021/5525591 ◽

2021 ◽

Vol 2021 ◽

pp. 1-6

Author(s):

Lahcen Ibnelazyz ◽

Karim Guida ◽

Khalid Hilal ◽

Said Melliani

Keyword(s):

Fixed Point ◽

Fixed Point Theory ◽

Point Theory ◽

Contraction Mapping Principle ◽

Integrodifferential Equations ◽

Krasnoselskii’S Fixed Point Theorem ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Banach Contraction ◽

Banach Contraction Mapping Principle

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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The continuation of solutions to systems of Caputo fractional order differential equations

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2020-0029 ◽

2020 ◽

Vol 23 (2) ◽

pp. 591-599 ◽

Cited By ~ 1

Author(s):

Cong Wu ◽

Xinzhi Liu

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Fractional Order ◽

Point Theorem ◽

Existence And Uniqueness ◽

Existence And Uniqueness Results ◽

Fractional Order Differential Equations ◽

Uniqueness Results ◽

Schäuder Fixed Point Theorem

AbstractIn this paper, we study the continuation of solutions to systems of Caputo fractional order differential equations. The continuation is constructed and proven by using the Schauder Fixed Point Theorem. As a necessary prerequisite to the continuation, the existence and uniqueness results generalized for systems are also reviewed.

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