scholarly journals Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Abdellatif Boutiara ◽  
Mohammed M. Matar ◽  
Mohammed K. A. Kaabar ◽  
Francisco Martínez ◽  
Sina Etemad ◽  
...  
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Existence And Uniqueness Results ◽  
New Class ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Functional Delay ◽  
Delay Differential ◽  
The Given ◽  
Existence Criteria

In this paper, a new class of a neutral functional delay differential equation involving the generalized ψ -Caputo derivative is investigated on a partially ordered Banach space. The existence and uniqueness results to the given boundary value problem are established with the help of the Dhage’s technique and Banach contraction principle. Also, we prove other existence criteria by means of the topological degree method. Finally, Ulam-Hyers type stability and its generalized version are studied. Two illustrative examples are presented to demonstrate the validity of our obtained results.

scholarly journals Solution Of Singularly Perturbed Delay Differential Equations Using Liouville Green Transformation

2021 ◽  
Vol 12 (4) ◽  
pp. 325-335
Author(s):  
M. Adilaxmi , Et. al.
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Perturbation Problem ◽  
Delay Differential ◽  
Singularly Perturbation ◽  
The Given

This paper envisages the use of Liouville Green Transformation to find the solution of singularly perturbed delay differential equations. First, using Taylor series, the given singularly perturbed delay differential equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. The method is demonstrated by implementing several model examples by taking various values for the delay parameter and perturbation parameter.

scholarly journals Fractional Differential Equation Involving Mixed Nonlinearities with Nonlocal Multi-Point and Riemann-Stieltjes Integral-Multi-Strip Conditions

2019 ◽  
Vol 3 (2) ◽  
pp. 34 ◽  
Author(s):  
Ahmad ◽  
Alsaedi ◽  
Salem ◽  
Ntouyas
Keyword(s):  
Fixed Point Theory ◽  
Point Theory ◽  
Stieltjes Integral ◽  
Existence And Uniqueness Results ◽  
New Class ◽  
Uniqueness Results ◽  
Special Cases ◽  
Mixed Nonlinearities ◽  
Fractional Differential ◽  
The Given

In this paper, we investigate a new class of boundary value problems involving fractionaldifferential equations with mixed nonlinearities, and nonlocal multi-point and Riemann–Stieltjesintegral-multi-strip boundary conditions. Based on the standard tools of the fixed point theory,we obtain some existence and uniqueness results for the problem at hand, which are well illustratedwith the aid of examples. Our results are not only in the given configuration but also yield severalnew results as special cases. Some variants of the given problem are also discussed.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
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.

scholarly journals A Langevin-Type q-Variant System of Nonlinear Fractional Integro-Difference Equations with Nonlocal Boundary Conditions

2022 ◽  
Vol 6 (1) ◽  
pp. 45
Author(s):  
Ravi P. Agarwal ◽  
Hana Al-Hutami ◽  
Bashir Ahmad
Keyword(s):  
Boundary Conditions ◽  
Difference Equations ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
New Class ◽  
Uniqueness Results ◽  
Multipoint Boundary Conditions ◽  
The Given ◽  
Variant System

We introduce a new class of boundary value problems consisting of a q-variant system of Langevin-type nonlinear coupled fractional integro-difference equations and nonlocal multipoint boundary conditions. We make use of standard fixed-point theorems to derive the existence and uniqueness results for the given problem. Illustrative examples for the obtained results are also presented.

scholarly journals Analysis of implicit type of a generalized fractional differential equations with nonlinear integral boundary conditions

2020 ◽  
Vol 1 (1) ◽  
pp. 64-76
Author(s):  
Saleh Redhwan ◽  
Sadikali Shaikh
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

The given paper describes the implicit fractional differential equation with nonlinear integral boundary conditions in the frame of Caputo-Katugampola fractional derivative. We obtain an analogous integral equation of the given problem and prove the existence and uniqueness results of such a problem using the Banach and Krasnoselskii fixed point theorems. To show the effectiveness of the acquired results, convenient examples are presented.

scholarly journals Smoothing the domain out for positive solutions

2000 ◽  
Vol 61 (3) ◽  
pp. 405-413 ◽  
Author(s):  
Yaping Liu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Nonlinear Partial Differential Equation ◽  
Irregular Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Analytical Tools ◽  
The Given

For a given nonlinear partial differential equation defined on a bounded domain with irregular boundary, the available analytical tools are very limited in relation to the study of positive solutions. In this paper wer first use weak convergence methods to show that for an elliptic equation of a certain type, classical positive solutions on nearby smooth domains approach a generalised positive solution on the given domain. The idea is then applied to sublinear elliptic problems to obtain existence and uniqueness results.

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.

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