scholarly journals Investigation of a Class of Implicit Anti-Periodic Boundary Value Problems

2021 ◽  
Vol 2 (1) ◽  
pp. 47-61
Author(s):  
Laila Hashtamand
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Fixed Point Theory ◽  
Periodic Boundary Conditions ◽  
Point Theory ◽  
Fractional Order Differential Equations ◽  
Periodic Boundary Value Problems ◽  
Stability Results

This research is devoted to studying a class of implicit fractional order differential equations ($\mathrm{FODEs}$) under anti-periodic boundary conditions ($\mathrm{APBCs}$). With the help of classical fixed point theory due to $\mathrm{Schauder}$ and $\mathrm{Banach}$, we derive some adequate results about the existence of at least one solution. Moreover, this manuscript discusses the concept of stability results including Ulam-Hyers (HU) stability, generalized Hyers-Ulam (GHU) stability, Hyers-Ulam Rassias (HUR) stability, and generalized Hyers-Ulam- Rassias (GHUR)stability. Finally, we give three examples to illustrate our results.

scholarly journals RIEMANN–LIOUVILLE FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH FRACTIONAL NONLOCAL MULTI-POINT BOUNDARY CONDITIONS

Fractals ◽  
2021 ◽  
pp. 2240002
Author(s):  
BASHIR AHMAD ◽  
BADRAH ALGHAMDI ◽  
RAVI P. AGARWAL ◽  
AHMED ALSAEDI
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Weighted Space ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fractional Integrals ◽  
Existence Theory ◽  
Uniqueness Of Solutions

In this paper, we investigate the existence and uniqueness of solutions for Riemann–Liouville fractional integro-differential equations equipped with fractional nonlocal multi-point and strip boundary conditions in the weighted space. The methods of our study include the well-known tools of the fixed point theory, which are commonly applied to establish the existence theory for the initial and boundary value problems after converting them into the fixed point problems. We also discuss the case when the nonlinearity depends on the Riemann–Liouville fractional integrals of the unknown function. Numerical examples illustrating the main results are presented.

scholarly journals A novel stability analysis for the Darboux problem of partial differential equations via fixed point theory

2021 ◽  
Vol 6 (11) ◽  
pp. 12894-12901
Author(s):  
El-sayed El-hady ◽  
◽  
Abdellatif Ben Makhlouf
Keyword(s):  
Fixed Point ◽  
Stability Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fixed Point Theory ◽  
Main Tool ◽  
Point Theory ◽  
Darboux Problem ◽  
Partial Differential ◽  
Stability Results

<abstract><p>We present Ulam-Hyers-Rassias (UHR) stability results for the Darboux problem of partial differential equations (DPPDEs). We employ some fixed point theorem (FPT) as the main tool in the analysis. In this manner, our results are considered as some generalized version of several earlier outcomes.</p></abstract>

scholarly journals Multiple Positive Solutions for Singular Periodic Boundary Value Problems of Impulsive Differential Equations in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Hongxia Fan ◽  
Yongxiang Li
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Point Theory ◽  
Singular Boundary ◽  
Multiple Positive Solutions ◽  
Periodic Boundary Value Problems

By means of the fixed point theory of strict set contraction operators, we establish a new existence theorem on multiple positive solutions to a singular boundary value problem for second-order impulsive differential equations with periodic boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.

scholarly journals Global existence and stability results for mild solutions of random impulsive partial integro-differential equations

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 439-455 ◽  
Author(s):  
A. Vinodkumar ◽  
P. Indhumathi
Keyword(s):  
Fixed Point ◽  
Global Existence ◽  
Differential Equations ◽  
Continuous Dependence ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Point Theory ◽  
Banach Contraction ◽  
Existence And Stability ◽  
Stability Results

In this paper, we discuss the global existence, uniqueness, continuous dependence and exponential stability of random impulsive partial integro-differential equations is investigated. The results are obtained by using the Leray-Schauder alternative fixed point theory and Banach Contraction Principle. Finally we give an example to illustrate our abstract results.

scholarly journals Boundary Value Problem for Caputo–Fabrizio Random Fractional Differential Equations

2020 ◽  
Vol 6 (2) ◽  
pp. 218-230
Author(s):  
Fouzia Bekada ◽  
Saïd Abbas ◽  
Mouffak Benchohra
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Random Operators ◽  
Ulam Stability ◽  
Fractional Differential ◽  
Stability Results

AbstractThis article deals with some existence of random solutions and Ulam stability results for a class of Caputo-Fabrizio random fractional differential equations with boundary conditions in Banach spaces. Our results are based on the fixed point theory and random operators. Two illustrative examples are presented in the last section.

scholarly journals Fractional-Order Integro-Differential Multivalued Problems with Fixed and Nonlocal Anti-Periodic Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1774 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Ravi P. Agarwal ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Fixed Point Theory ◽  
Periodic Boundary Conditions ◽  
Point Theory ◽  
Caputo Fractional Derivatives ◽  
New Class ◽  
Fractional Differential ◽  
The Given ◽  
Derivatives Of

This paper studies a new class of fractional differential inclusions involving two Caputo fractional derivatives of different orders and a Riemann–Liouville type integral nonlinearity, supplemented with a combination of fixed and nonlocal (dual) anti-periodic boundary conditions. The existence results for the given problem are obtained for convex and non-convex cases of the multi-valued map by applying the standard tools of the fixed point theory. Examples illustrating the obtained results are presented.

scholarly journals Existence of solutions or nonlinear nth-order differential equations and inclusions with nonlocal and integral boundary conditions via fixed point theory

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2149-2162 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris Ntouyas ◽  
Hamed Alsulami
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Differential Equations And Inclusions

In this paper, a class of boundary value problems of nonlinear nth-order differential equations and inclusions with nonlocal and integral boundary conditions is studied. New existence results are obtained by means of some fixed point theorems. Examples are given for the illustration of the results.

scholarly journals Existence of One-Signed Solutions of Discrete Second-Order Periodic Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Ruyun Ma ◽  
Yanqiong Lu ◽  
Tianlan Chen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Nonlinear Difference Equation ◽  
Periodic Boundary Value Problems ◽  
The Fixed Point Theorem

We prove the existence of one-signed periodic solutions of second-order nonlinear difference equation on a finite discrete segment with periodic boundary conditions by combining some properties of Green's function with the fixed-point theorem in cones.

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