Existence and uniqueness of solutions to fractional Langevin equations involving two fractional orders

2018 ◽  
Vol 20 (2) ◽  
Author(s):  
Hamid Baghani
Keyword(s):  
Existence And Uniqueness ◽  
Langevin Equations ◽  
Uniqueness Of Solutions ◽  
Fractional Orders

scholarly journals On fractional Langevin equation involving two fractional orders in different intervals

2019 ◽  
Vol 24 (6) ◽  
Author(s):  
Hamid Baghani ◽  
J. Nieto
Keyword(s):  
Langevin Equation ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Numerical Examples ◽  
Fractional Equations ◽  
Fractional Langevin Equation ◽  
Nonlinear Langevin Equation ◽  
Fractional Orders

In this paper, we study a nonlinear Langevin equation involving two fractional orders  α ∈ (0; 1] and β ∈ (1; 2] with initial conditions. By means of an interesting fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. Some illustrative numerical examples are also discussed. 

scholarly journals Uniqueness and existence of solutions for nonlinear fractional differential equations with two fractional orders

Mathematica ◽  
2021 ◽  
Vol 63 (86) (2) ◽  
pp. 254-267
Author(s):  
Mohamed Houas ◽  
◽  
Zoubir Dahmani ◽  
Erhan Set ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Degree Theory ◽  
Uniqueness Of Solutions ◽  
Nonlinear Alternative ◽  
Banach’S Fixed Point Theorem ◽  
Fractional Differential ◽  
Uniqueness And Existence ◽  
Fractional Orders

We study the existence and uniqueness of solutions for integro-differential equations involving two fractional orders. By using the Banach’s fixed point theorem, Leray-Schauder’s nonlinear alternative and Leray-Schauder’s degree theory, the existence and uniqueness of solutions are obtained. Some illustrative examples are also presented.

scholarly journals Existence and Numerical Simulation of Solutions for Fractional Equations Involving Two Fractional Orders with Nonlocal Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Jing Zhao ◽  
Peifen Lu ◽  
Yiliang Liu
Keyword(s):  
Numerical Simulation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Nonlocal Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Fractional Equations ◽  
Fractional Langevin Equation ◽  
Fractional Orders

We study a boundary value problem for fractional equations involving two fractional orders. By means of a fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. In addition, we describe the dynamic behaviors of the fractional Langevin equation by using theG2algorithm.

scholarly journals Theoretical and numerical analysis for transmission dynamics of COVID-19 mathematical model involving Caputo–Fabrizio derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sabri T. M. Thabet ◽  
Mohammed S. Abdo ◽  
Kamal Shah
Keyword(s):  
Mathematical Model ◽  
Existence And Uniqueness ◽  
Approximate Solutions ◽  
Transmission Dynamics ◽  
Uniqueness Of Solutions ◽  
Proposed Model ◽  
The Laplace Transform ◽  
Theoretical And Numerical Analysis ◽  
Fractional Orders ◽  
Kernel Type

AbstractThis manuscript is devoted to a study of the existence and uniqueness of solutions to a mathematical model addressing the transmission dynamics of the coronavirus-19 infectious disease (COVID-19). The mentioned model is considered with a nonsingular kernel type derivative given by Caputo–Fabrizo with fractional order. For the required results of the existence and uniqueness of solution to the proposed model, Picard’s iterative method is applied. Furthermore, to investigate approximate solutions to the proposed model, we utilize the Laplace transform and Adomian’s decomposition (LADM). Some graphical presentations are given for different fractional orders for various compartments of the model under consideration.

Integral Representations for the Solution of Dynamic Bending of a Plate with Displacement-Traction Boundary Data

2003 ◽  
Vol 10 (3) ◽  
pp. 467-480
Author(s):  
Igor Chudinovich ◽  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Boundary Data ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Boundary Integral ◽  
Integral Representations ◽  
Transverse Shear Deformation ◽  
Uniqueness Of Solutions ◽  
Nonstationary Boundary

Abstract The existence of distributional solutions is investigated for the time-dependent bending of a plate with transverse shear deformation under mixed boundary conditions. The problem is then reduced to nonstationary boundary integral equations and the existence and uniqueness of solutions to the latter are studied in appropriate Sobolev spaces.

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