scholarly journals Existence and uniqueness results for nonlinear implicit Riemann-Liouville fractional differential equations with nonlocal conditions

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4881-4891
Author(s):  
Adel Lachouri ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

In this paper, we use the fixed point theory to obtain the existence and uniqueness of solutions for nonlinear implicit Riemann-Liouville fractional differential equations with nonlocal conditions. An example is given to illustrate this work.

scholarly journals EXISTENCE AND UNIQUENESS RESULTS FOR A COUPLED SYSTEM OF HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTI-POINT BOUNDARY CONDITIONS

2020 ◽  
pp. 843
Author(s):  
Mohamed Houas ◽  
Khellaf Ould Melha
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

In this paper, we have studied existence and uniqueness of solutions for a coupled system of multi-point boundary value problems for Hadamard fractional differential equations. By applying principle contraction and Shaefer's fixed point theorem new existence results have been obtained.

scholarly journals Study of a Class of Generalized Multiterm Fractional Differential Equations with Generalized Fractional Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Wafa Shammakh ◽  
Hadeel Z. Alzumi ◽  
Zahra Albarqi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

The aim of this work is to study the new generalized fractional differential equations involving generalized multiterms and equipped with multipoint boundary conditions. The nonlinear term is taken from Orlicz space. The existence and uniqueness results, with the help of contemporary tools of fixed point theory, are investigated. The Ulam stability of our problem is also presented. The obtained results are well illustrated by examples.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

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.

scholarly journals Existence results for coupled nonlinear fractional differential equations of different orders with nonlocal coupled boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed Alsaedi ◽  
Soha Hamdan ◽  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Arbitrary Domain ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Coupled Boundary Conditions ◽  
Fractional Differential

AbstractThis paper is concerned with the solvability of coupled nonlinear fractional differential equations of different orders supplemented with nonlocal coupled boundary conditions on an arbitrary domain. The tools of the fixed point theory are applied to obtain the criteria ensuring the existence and uniqueness of solutions of the problem at hand. Examples illustrating the main results are presented.

scholarly journals A Note on Fractional Differential Equations with Fractional Separated Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
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.

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

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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