scholarly journals Existence results for coupled system of nonlinear differential equations and inclusions involving sequential derivatives of fractional order

2021 ◽  
Vol 7 (1) ◽  
pp. 723-755
Author(s):  
M. Manigandan ◽  
◽  
Subramanian Muthaiah ◽  
T. Nandhagopal ◽  
R. Vadivel ◽  
...  
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Nonlinear Differential Equations ◽  
Coupled System ◽  
Existence Results ◽  
Numerical Examples ◽  
Differential Equations And Inclusions ◽  
Derivatives Of

<abstract><p>In this article, we investigate new results of existence and uniqueness for systems of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order and along with new kinds of coupled discrete (multi-points) and fractional integral (Riemann-Liouville) boundary conditions. Our investigation is mainly based on the theorems of Schaefer, Banach, Covitz-Nadler, and nonlinear alternatives for Kakutani. The validity of the obtained results is demonstrated by numerical examples.</p></abstract>

scholarly journals Existence results for a coupled system of Caputo type fractional integro-differential equations with multi-point and sub-strip boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed Alsaedi ◽  
Amjad F. Albideewi ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Coupled System ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Integral Type ◽  
Uniqueness Of Solutions ◽  
Terminal Position

AbstractThis paper is concerned with the existence and uniqueness of solutions for a coupled system of Liouville–Caputo type fractional integro-differential equations with multi-point and sub-strip boundary conditions. The fractional integro-differential equations involve Caputo derivative operators of different orders and finitely many Riemann–Liouville fractional integral and non-integral type nonlinearities. The boundary conditions at the terminal position $t=1$ t = 1 involve sub-strips and multi-point contributions. The Banach fixed point theorem and the Leray–Schauder alternative are used to establish our results. The obtained results are illustrated with the aid of examples.

scholarly journals An Integral Operational Matrix of Fractional-Order Chelyshkov Functions and Its Applications

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1755
Author(s):  
M. S. Al-Sharif ◽  
A. I. Ahmed ◽  
M. S. Salim
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Operational Matrix ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Science And Engineering ◽  
Numerical Examples ◽  
Fractional Differential

Fractional differential equations have been applied to model physical and engineering processes in many fields of science and engineering. This paper adopts the fractional-order Chelyshkov functions (FCHFs) for solving the fractional differential equations. The operational matrices of fractional integral and product for FCHFs are derived. These matrices, together with the spectral collocation method, are used to reduce the fractional differential equation into a system of algebraic equations. The error estimation of the presented method is also studied. Furthermore, numerical examples and comparison with existing results are given to demonstrate the accuracy and applicability of the presented method.

scholarly journals QUALITATIVE STUDY OF NONLINEAR COUPLED PANTOGRAPH DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040045 ◽  
Author(s):  
ISRAR AHAMAD ◽  
KAMAL SHAH ◽  
THABET ABDELJAWAD ◽  
FAHD JARAD
Keyword(s):  
Fixed Point ◽  
Qualitative Study ◽  
Differential Equations ◽  
Nonlinear Analysis ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Main Work ◽  
Nonlinear Coupled System

In this paper, we investigate a nonlinear coupled system of fractional pantograph differential equations (FPDEs). The respective results address some adequate results for existence and uniqueness of solution to the problem under consideration. In light of fixed point theorems like Banach and Krasnoselskii’s, we establish the required results. Considering the tools of nonlinear analysis, we develop some results regarding Ulam–Hyers (UH) stability. We give three pertinent examples to demonstrate our main work.

scholarly journals Results for Mild solution of fractional coupled hybrid boundary value problems

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Hossein Jafari ◽  
Hasib Khan ◽  
Sarah Jane Johnston
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Mild Solution ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Coupled System ◽  
Banach Contraction ◽  
Fractional Differential

AbstractThe study of coupled system of hybrid fractional differential equations (HFDEs) needs the attention of scientists for the exploration of its different important aspects. Our aim in this paper is to study the existence and uniqueness of mild solution (EUMS) of a coupled system of HFDEs. The novelty of this work is the study of a coupled system of fractional order hybrid boundary value problems (HBVP) with n initial and boundary hybrid conditions. For this purpose, we are utilizing some classical results, Leray–Schauder Alternative (LSA) and Banach Contraction Principle (BCP). Some examples are given for the illustration of applications of our results.

A coupled system of nonlinear differential equations involving m nonlinear terms

2016 ◽  
Vol 23 (3) ◽  
pp. 447-458 ◽  
Author(s):  
Amele Taieb ◽  
Zoubir Dahmani
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Coupled System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Schaefer Fixed Point Theorem ◽  
Fractional Differential ◽  
The Banach Contraction Principle

AbstractIn this paper, we study a coupled system of nonlinear fractional differential equations involving m nonlinear terms, ${m\in\mathbb{N^{*}}}$. We begin by introducing a new Banach space. Then, we establish new existence and uniqueness results using the Banach contraction principle. We also prove an existence result using the Schaefer fixed point theorem. Finally, we give some illustrative examples.

scholarly journals Existence results for coupled differential equations of non-integer order with Riemann-Liouville, Erdélyi-Kober integral conditions

2021 ◽  
Vol 6 (12) ◽  
pp. 13004-13023
Author(s):  
Dumitru Baleanu ◽  
◽  
S. Hemalatha ◽  
P. Duraisamy ◽  
P. Pandiyan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Integral Conditions ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Uniqueness Of A Solution

<abstract><p>This paper proposes the existence and uniqueness of a solution for a coupled system that has fractional differential equations through Erdélyi-Kober and Riemann-Liouville fractional integral boundary conditions. The existence of the solution for the coupled system by adopting the Leray-Schauder alternative. The uniqueness of solution for the problem can be found using Banach fixed point theorem. In order to verify the proposed criterion, some numerical examples are also discussed.</p></abstract>

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