scholarly journals On time fractional pseudo-parabolic equations with nonlocal integral conditions

2020 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nguyen Anh Tuan ◽  
Donal O'Regan ◽  
Dumitru Baleanu ◽  
Nguyen H. Tuan
Keyword(s):  
Parabolic Equations ◽  
Integral Conditions ◽  
Nonlocal Integral Conditions

On time fractional pseudo‐parabolic equations with nonlocal integral conditions

2021 ◽  
Author(s):  
Nguyen Huu Can ◽  
Devendra Kumar ◽  
Tri Vo Viet ◽  
Anh Tuan Nguyen
Keyword(s):  
Parabolic Equations ◽  
Integral Conditions ◽  
Nonlocal Integral Conditions

scholarly journals A nonlinear fractional Rayleigh–Stokes equation under nonlocal integral conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nguyen Hoang Luc ◽  
Le Dinh Long ◽  
Ho Thi Kim Van ◽  
Van Thinh Nguyen
Keyword(s):  
Exact Solution ◽  
Convergence Rate ◽  
Stokes Equation ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Integral Conditions ◽  
Initial Value ◽  
Truncation Method ◽  
Nonlocal Integral Conditions ◽  
Regularized Solution

AbstractIn this paper, we study the fractional nonlinear Rayleigh–Stokes equation under nonlocal integral conditions, and the existence and uniqueness of the mild solution to our problem are considered. The ill-posedness of the mild solution to the problem recovering the initial value is also investigated. To tackle the ill-posedness, a regularized solution is constructed by the Fourier truncation method, and the convergence rate to the exact solution of this method is demonstrated.

scholarly journals Multi-Strip and Multi-Point Boundary Conditions for Fractional Langevin Equation

2020 ◽  
Vol 4 (2) ◽  
pp. 18 ◽  
Author(s):  
Ahmed Salem ◽  
Balqees Alghamdi
Keyword(s):  
Fixed Point ◽  
Langevin Equation ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Integral Conditions ◽  
Fractional Langevin Equation ◽  
Uniqueness Of The Solution ◽  
Nonlocal Integral Conditions ◽  
Nonlinear Langevin Equation

In the present paper, we discuss a new boundary value problem for the nonlinear Langevin equation involving two distinct fractional derivative orders with multi-point and multi-nonlocal integral conditions. The fixed point theorems for Schauder and Krasnoselskii–Zabreiko are applied to study the existence results. The uniqueness of the solution is given by implementing the Banach fixed point theorem. Some examples showing our basic results are provided.

scholarly journals Non-local Problems with Integral Displacement for Highorder Parabolic Equations

2021 ◽  
Vol 36 ◽  
pp. 14-28
Author(s):  
A.I. Kozhanov ◽  
◽  
A.V. Dyuzheva ◽  
◽  
Keyword(s):  
Parabolic Equations ◽  
High Order ◽  
Multidimensional Case ◽  
Integral Conditions ◽  
Spatial Variables ◽  
One Dimensional ◽  
Linear Parabolic Equations ◽  
Local Problems ◽  
Non Local ◽  
The One

The aim of this paper is to study the solvability of solutions of non-local problems with integral conditions in spatial variables for high-order linear parabolic equations in the classes of regular solutions (which have all the squared derivatives generalized by S. L. Sobolev that are included in the corresponding equation) . Previously, similar problems were studied for high-order parabolic equations, either in the one-dimensional case, or when certain conditions of smallness on the coefficients are met equations. In this paper, we present new results on the solvability of non-local problems with integral spatial variables for high-order parabolic equations a) in the multidimensional case with respect to spatial variables; b) in the absence of smallness conditions. The research method is based on the transition from a problem with non-local integral conditions to a problem with classical homogeneous conditions of the first or second kind on the side boundary for a loaded integro-differential equation. At the end of the paper, some generalizations of the obtained results will be described.

scholarly journals Existence, uniqueness and numerical solution of a fractional PDE with integral conditions

2019 ◽  
Vol 24 (3) ◽  
pp. 368-386
Author(s):  
Jesus Martín-Vaquero ◽  
Ahcene Merad
Keyword(s):  
Existence And Uniqueness ◽  
Recent Literature ◽  
Numerical Approach ◽  
Integral Conditions ◽  
Fractional Partial Differential Equation ◽  
One Dimensional ◽  
Fractional Pde ◽  
Uniqueness Of The Solution ◽  
Nonlocal Integral Conditions ◽  
Hereditary Properties

This paper is devoted to the solution of one-dimensional Fractional Partial Differential Equation (FPDE) with nonlocal integral conditions. These FPDEs have been of considerable interest in the recent literature because fractional-order derivatives and integrals enable the description of the memory and hereditary properties of different substances. Existence and uniqueness of the solution of this FPDE are demonstrated. As for the numerical approach, a Galerkin method based on least squares is considered. The numerical examples illustrate the fast convergence of this technique and show the efficiency of the proposed method.

scholarly journals Uniqueness of Solutions, Stability and Simulations for a Differential Problem Involving Convergent Series and Time Variable Singularities

2021 ◽  
Author(s):  
Yazid GOUARI ◽  
Zoubir Dahmani ◽  
Meriem Mansouria BELHAMITI ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Convergent Series ◽  
Time Variable ◽  
Kutta Method ◽  
Integral Conditions ◽  
Uniqueness Of Solutions ◽  
Differential Problem ◽  
New Type ◽  
Nonlocal Integral Conditions

We focus on a new type of nonlinear integro-differential equations with nonlocal integral conditions. The considered problem has one nonlinearity with time variable singularity. It involves also some convergent series combined to Riemann-Liouville integrals. We prove a uniqueness of solutions for the proposed problem, then, we provide some examples to illustrate this result. Also, we discuss the Ulam-Hyers stability for the problem. Some numerical simulations, using Rung Kutta method, are discussed too. At the end, a conclusion follows.

scholarly journals Numerical Analysis of the Eigenvalue Problem for One-Dimensional Differential Operator with Nonlocal Integral Conditions

2009 ◽  
Vol 14 (1) ◽  
pp. 115-122 ◽  
Author(s):  
S. Sajavičius ◽  
M. Sapagovas
Keyword(s):  
Numerical Analysis ◽  
Differential Operator ◽  
Eigenvalue Problem ◽  
General Problem ◽  
Nonlocal Conditions ◽  
Spectral Structure ◽  
Integral Conditions ◽  
One Dimensional ◽  
Special Cases ◽  
Nonlocal Integral Conditions

In this paper the eigenvalue problem for one-dimensional differential operator with nonlocal integral conditions is investigated numerically. The special cases of general problem are analyzed and hypothesis about the dependence of the spectral structure of that problem on the coefficient of differential operator and the parameters of nonlocal conditions are formulated.

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