scholarly journals Existence of a Solution of a Certain Volterra –Fredholm Integro Differential Equations

2012 ◽  
Vol 25 (3) ◽  
pp. 62-67
Author(s):  
Akram H. Mahmood ◽  
Lamyaa H. Sadoon
Keyword(s):  
Differential Equations ◽  
Existence Of A Solution

Approximate controllability of non-instantaneous impulsive semilinear measure driven control system with infinite delay via fundamental solution

2020 ◽  
Author(s):  
Surendra Kumar ◽  
Syed Mohammad Abdal
Keyword(s):  
Fundamental Solution ◽  
Differential Equations ◽  
Control Systems ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Existence Of A Solution ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
New Class

Abstract This article investigates a new class of non-instantaneous impulsive measure driven control systems with infinite delay. The considered system covers a large class of the hybrid system without any restriction on their Zeno behavior. The concept of measure differential equations is more general as compared to the ordinary impulsive differential equations; consequently, the discussed results are more general than the existing ones. In particular, using the fundamental solution, Krasnoselskii’s fixed-point theorem and the theory of Lebesgue–Stieltjes integral, a new set of sufficient conditions is constructed that ensures the existence of a solution and the approximate controllability of the considered system. Lastly, an example is constructed to demonstrate the effectiveness of obtained results.

scholarly journals On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Dongming Nie ◽  
Azmat Ullah Khan Niazi ◽  
Bilal Ahmed
Keyword(s):  
Differential Equations ◽  
Existence Of A Solution ◽  
Neutral Differential Equations ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Functional Differential ◽  
Schauder Theorem ◽  
Equations With Delay ◽  
Rassias Stability ◽  
Fractional Functional

We discuss the existence of positive solution for a class of nonlinear fractional differential equations with delay involving Caputo derivative. Well-known Leray–Schauder theorem, Arzela–Ascoli theorem, and Banach contraction principle are used for the fixed point property and existence of a solution. We establish local generalized Ulam–Hyers stability and local generalized Ulam–Hyers–Rassias stability for the same class of nonlinear fractional neutral differential equations. The simulation of an example is also given to show the applicability of our results.

Boundary value problems for systems of second order differential equations

1985 ◽  
Vol 101 (1-2) ◽  
pp. 61-76 ◽  
Author(s):  
L. H. Erbe ◽  
H. W. Knobloch
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Existence Of A Solution ◽  
Differential Systems ◽  
Second Order Differential Equations

SynopsisWe consider boundary value problems for second order differential systems of the form (1)x” = A(t)x′ + f(t, x) and (2) x” = A(t)x′ + f(t, x) + q(t, x). By assuming the existence of a solution to (1) with a given region in (t, x) space, we derive conditions under which there exists a solution to (2) which stays in a certain neighbourhood of and satisfies given boundary conditions.

Conjugate points for fractional differential equations

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Paul Eloe ◽  
Jeffrey Neugebauer
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Conjugate Point ◽  
Sufficient Conditions ◽  
Conjugate Points ◽  
Existence Of A Solution ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential ◽  
Linear Differential

AbstractLet b > 0. Let 1 < α ≤ 2. The theory of u 0-positive operators with respect to a cone in a Banach space is applied to study the conjugate boundary value problem for Riemann-Liouville fractional linear differential equations D 0+α u + λp(t)u = 0, 0 < t < b, satisfying the conjugate boundary conditions u(0) = u(b) = 0. The first extremal point, or conjugate point, of the conjugate boundary value problem is defined and criteria are established to characterize the conjugate point. As an application, a fixed point theorem is applied to give sufficient conditions for existence of a solution of a related boundary value problem for a nonlinear fractional differential equation.

scholarly journals Travelling wave solutions for rich flames of reactive suspensions

1988 ◽  
Vol 30 (1) ◽  
pp. 89-100 ◽  
Author(s):  
K. K. Tam
Keyword(s):  
Approximate Solution ◽  
Eigenvalue Problem ◽  
Differential Equations ◽  
Shooting Method ◽  
Nonlinear Eigenvalue Problem ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Existence Of A Solution ◽  
Wave Solutions ◽  
The Given

AbstractThe modelling of the combustion of dust suspensions leads to a nonlinear eigenvalue problem for a system of ordinary differential equations defined over an infinite interval. The equations contain a number of parameters. In this study, the shooting method is used to prove the existence of a solution. Linearisation is then used to provide an approximate solution, from which an estimate of the eigenvalue and its dependence on the given parameters can be obtained.

scholarly journals Existence of solution for Mean-field Reflected Discontinuous Backward Doubly Stochastic Differential Equation

2020 ◽  
Vol 5 (2) ◽  
pp. 205-216
Author(s):  
Mostapha Abdelouahab Saouli
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Mean Field ◽  
Existence Of Solution ◽  
Maximal Solution ◽  
Existence Of A Solution ◽  
Doubly Stochastic

AbstractIn this paper we prove the existence of a solution for mean-field reflected backward doubly stochastic differential equations (MF-RBDSDEs) with one continuous barrier and discontinuous generator (left-continuous). By a comparison theorem establish here for MF-RBDSDEs, we provide a minimal or a maximal solution to MF-RBDSDEs.

QUANTUM STOCHASTIC ANALYSIS VIA WHITE NOISE OPERATORS IN WEIGHTED FOCK SPACE

2002 ◽  
Vol 14 (03) ◽  
pp. 241-272 ◽  
Author(s):  
DONG MYUNG CHUNG ◽  
UN CIG JI ◽  
NOBUAKI OBATA
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
White Noise ◽  
Fock Space ◽  
Existence Of A Solution ◽  
Quantum Stochastic Differential Equation ◽  
Unique Existence ◽  
Regularity Properties ◽  
Weighted Fock Space ◽  
White Noises

White noise theory allows to formulate quantum white noises explicitly as elemental quantum stochastic processes. A traditional quantum stochastic differential equation of Itô type is brought into a normal-ordered white noise differential equation driven by lower powers of quantum white noises. The class of normal-ordered white noise differential equations covers quantum stochastic differential equations with highly singular noises such as higher powers or higher order derivatives of quantum white noises, which are far beyond the traditional Itô theory. For a general normal-ordered white noise differential equation unique existence of a solution is proved in the sense of white noise distribution. Its regularity properties are investigated by means of weighted Fock spaces interpolating spaces of white noise distributions and associated characterization theorems for S-transform and for operator symbols.

scholarly journals Applications of Krasnoselskii-Dhage Type Fixed-Point Theorems to Fractional Hybrid Differential Equations

2021 ◽  
Vol 52 ◽  
Author(s):  
Habibulla Akhadkulov ◽  
Fahad Alsharari ◽  
Teh Yuan Ying
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Integral Operators ◽  
Existence Of A Solution ◽  
Hybrid Differential Equation ◽  
Hybrid Differential Equations

In this paper, we prove the existence of a solution of a fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators by utilizing a new version of Kransoselskii-Dhage type fixed-point theorem obtained in [13]. Moreover, we provide an example to support our result.

scholarly journals A New Class of ψ -Caputo Fractional Differential Equations and Inclusion

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Wafa Shammakh ◽  
Hadeel Z. Alzumi ◽  
Bushra A. AlQahtani
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Research Work ◽  
Point Theory ◽  
Stieltjes Integral ◽  
Existence Of A Solution ◽  
New Class ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

In the present research work, we investigate the existence of a solution for new boundary value problems involving fractional differential equations with ψ -Caputo fractional derivative supplemented with nonlocal multipoint, Riemann–Stieltjes integral and ψ -Riemann–Liouville fractional integral operator of order γ boundary conditions. Also, we study the existence result for the inclusion case. Our results are based on the modern tools of the fixed-point theory. To illustrate our results, we provide examples.

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