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

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 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 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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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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Multi-term fractional differential equations with nonlocal boundary conditions

Open Mathematics ◽

10.1515/math-2018-0127 ◽

2018 ◽

Vol 16 (1) ◽

pp. 1519-1536

Author(s):

Bashir Ahmad ◽

Najla Alghamdi ◽

Ahmed Alsaedi ◽

Sotiris K. Ntouyas

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Nonlocal Boundary ◽

Nonlocal Boundary Conditions ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Fractional Differential ◽

The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

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A Note on Fractional Differential Equations with Fractional Separated Boundary Conditions

Abstract and Applied Analysis ◽

10.1155/2012/818703 ◽

2012 ◽

Vol 2012 ◽

pp. 1-11 ◽

Cited By ~ 16

Author(s):

Bashir Ahmad ◽

Sotiris K. Ntouyas

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Existence And Uniqueness Results ◽

New Class ◽

Uniqueness Results ◽

Separated Boundary Conditions ◽

Fractional Differential

We consider a new class of boundary value problems of nonlinear fractional differential equations with fractional separated boundary conditions. A connection between classical separated and fractional separated boundary conditions is developed. Some new existence and uniqueness results are obtained for this class of problems by using standard fixed point theorems. Some illustrative examples are also discussed.

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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 and Uniqueness with Ulam Stability study of the solution for a class of Caputo fractional integro-differential equation with mixed conditions

10.22541/au.161133857.79110223/v1 ◽

2021 ◽

Author(s):

ABDELLOUAHAB Naimi

Keyword(s):

Differential Equation ◽

Fixed Point ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Stability Study ◽

Ulam Stability ◽

Differential Problem ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Stability Results

In this article we show the existence, uniqueness and Ulam stability results of the solution for a class of a nonlinear Caputo fractional integro-differential problem with mixed conditions. we use three fixed point theorems to proof the existence and uniqueness results. By the results obtained, the reasons for the Ulam stability are verified. An example proposed to illustrate our main results.

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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 Ulam–Hyers Stability of a Fractional-Order Coupled System in the Frame of Generalized Hilfer Derivatives

Mathematics ◽

10.3390/math9202543 ◽

2021 ◽

Vol 9 (20) ◽

pp. 2543

Author(s):

Abdulkafi M. Saeed ◽

Mohammed S. Abdo ◽

Mdi Begum Jeelani

Keyword(s):

Fixed Point ◽

Fractional Order ◽

Existence And Uniqueness ◽

Fractional Derivatives ◽

Fixed Point Theorems ◽

Coupled System ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Special Cases ◽

Stability Of The Solution

In this research paper, we consider a class of a coupled system of fractional integrodifferential equations in the frame of Hilfer fractional derivatives with respect to another function. The existence and uniqueness results are obtained in weighted spaces by applying Schauder’s and Banach’s fixed point theorems. The results reported here are more general than those found in the literature, and some special cases are presented. Furthermore, we discuss the Ulam–Hyers stability of the solution to the proposed system. Some examples are also constructed to illustrate and validate the main 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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