Existence of the Class of Nonlinear Hybrid Fractional Langevin Quantum Differential Equation with Dirichlet Boundary Conditions

2021 ◽  
Vol 5 (4) ◽  
pp. 156
Author(s):  
Nagamanickam Nagajothi ◽  
Vadivel Sadhasivam ◽  
Omar Bazighifan ◽  
Rami Ahmad El-Nabulsi
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Contraction Mapping ◽  
Dirichlet Boundary ◽  
Contraction Mapping Principle ◽  
Existence Results ◽  
Dirichlet Boundary Conditions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Orders ◽  
Nonlinear Hybrid

In this paper, we investigate the existence results for nonlinear fractional q-difference equations with two different fractional orders supplemented with the Dirichlet boundary conditions. Our main existence results are obtained by applying the contraction mapping principle and Krasnoselskii’s fixed point theorem. An illustrative example is also discussed.

scholarly journals Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Bashir Ahmad ◽  
Juan J. Nieto
Keyword(s):  
Langevin Equation ◽  
Dirichlet Boundary ◽  
Contraction Mapping Principle ◽  
Dirichlet Boundary Conditions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Single Index ◽  
New Type ◽  
Nonlinear Langevin Equation ◽  
Physical Phenomena ◽  
Fractional Orders

We study a Dirichlet boundary value problem for Langevin equation involving two fractional orders. Langevin equation has been widely used to describe the evolution of physical phenomena in fluctuating environments. However, ordinary Langevin equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractal medium, numerous generalizations of Langevin equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Langevin equation. This gives rise to the fractional Langevin equation with a single index. Recently, a new type of Langevin equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.

scholarly journals Weak Solutions for ap-Laplacian Impulsive Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Wei Dong ◽  
Jiafa Xu ◽  
Xiaoyan Zhang
Keyword(s):  
Differential Equation ◽  
Variational Method ◽  
Boundary Conditions ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Impulsive Differential Equation ◽  
Dirichlet Boundary ◽  
Point Theory ◽  
Existence Results ◽  
Dirichlet Boundary Conditions

By the virtue of variational method and critical point theory, we give some existence results of weak solutions for ap-Laplacian impulsive differential equation with Dirichlet boundary conditions.

scholarly journals Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Bashir Ahmad ◽  
Juan J. Nieto
Keyword(s):  
Differential Equation ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Contraction Mapping Principle ◽  
Existence Results ◽  
Nonlocal Boundary Value Problem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

We study some existence results in a Banach space for a nonlocal boundary value problem involving a nonlinear differential equation of fractional orderqgiven bycDqx(t)=f(t,x(t)),0<t<1,q∈(m−1,m],m∈ℕ,m≥2, x(0)=0, x′(0)=0, x′′(0)=0,…,x(m−2)(0)=0,x(1)=αx(η). Our results are based on the contraction mapping principle and Krasnoselskii's fixed point theorem.

Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation

2008 ◽  
Vol 15 (3) ◽  
pp. 531-539
Author(s):  
Temur Jangveladze ◽  
Zurab Kiguradze
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Conditions ◽  
Large Time ◽  
Dirichlet Boundary ◽  
Large Time Behavior ◽  
Dirichlet Boundary Conditions ◽  
Time Behavior ◽  
Integro Differential Equation ◽  
Homogeneous Data

Abstract Large time behavior of solutions to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. The rate of convergence is given, too. Dirichlet boundary conditions with homogeneous data are considered.

scholarly journals EXISTENCE AND STABILITY ANALYSIS OF SOLUTIONS FOR FRACTIONAL LANGEVIN EQUATION WITH NONLOCAL INTEGRAL AND ANTI-PERIODIC-TYPE BOUNDARY CONDITIONS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040006 ◽  
Author(s):  
AMITA DEVI ◽  
ANOOP KUMAR ◽  
THABET ABDELJAWAD ◽  
AZIZ KHAN
Keyword(s):  
Boundary Conditions ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Banach Contraction ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Type Boundary ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

In this paper, we deal with the existence and uniqueness (EU) of solutions for nonlinear Langevin fractional differential equations (FDE) having fractional derivative of different orders with nonlocal integral and anti-periodic-type boundary conditions. Also, we investigate the Hyres–Ulam (HU) stability of solutions. The existence result is derived by applying Krasnoselskii’s fixed point theorem and the uniqueness of result is established by applying Banach contraction mapping principle. An example is offered to ensure the validity of our obtained results.

Multiplicity and Existence Results for a Nonlinear Elliptic Equation With Sobolev Exponent

2010 ◽  
Vol 10 (3) ◽  
Author(s):  
Zakaria Bouchech ◽  
Hichem Chtioui
Keyword(s):  
Elliptic Equation ◽  
Boundary Conditions ◽  
Nonlinear Elliptic Equation ◽  
Dirichlet Boundary ◽  
Existence Results ◽  
Dirichlet Boundary Conditions ◽  
Nonlinear Elliptic ◽  
Sobolev Exponent

AbstractIn this paper we consider the following nonlinear elliptic equation with Dirichlet boundary conditions: -Δu = K(x)u

scholarly journals On a Differential Inclusion Involving Dirichlet–Laplace Operators of Fractional Orders

2020 ◽  
Vol 43 (6) ◽  
pp. 4089-4106
Author(s):  
Rafał Kamocki
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusion ◽  
Laplace Operator ◽  
Spectral Decomposition ◽  
Convex Analysis ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Fenchel Transform ◽  
The Laplace Operator ◽  
Fractional Orders

Abstract In this paper, we investigate a nonlinear differential inclusion with Dirichlet boundary conditions containing a weak Laplace operator of fractional orders (defined via the spectral decomposition of the Laplace operator $$-{\varDelta }$$ - Δ under Dirichlet boundary conditions). Using variational methods, we characterize solutions of such a problem. Our approach is based on tools from convex analysis (properties of a Legendre–Fenchel transform).

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