scholarly journals On a backward problem for two-dimensional time fractional wave equation with discrete random data

2020 ◽  
Vol 9 (2) ◽  
pp. 561-579
Author(s):  
Nguyen Huy Tuan ◽  
◽  
Tran Ngoc Thach ◽  
Yong Zhou ◽  
◽  
...  
Keyword(s):  
Wave Equation ◽  
Two Dimensional ◽  
Random Data ◽  
Fractional Wave Equation ◽  
Backward Problem ◽  
Time Fractional Wave Equation

On a backward problem for nonlinear time fractional wave equations

2021 ◽  
pp. 1-24
Author(s):  
Jia Wei He ◽  
Yong Zhou
Keyword(s):  
Wave Equation ◽  
Regularization Method ◽  
Existence And Uniqueness ◽  
Wave Equations ◽  
Mild Solutions ◽  
Fractional Wave Equation ◽  
Backward Problem ◽  
Fractional Wave Equations ◽  
Time Fractional Wave Equation ◽  
Eigenvalue Expansion

In this paper, we concern with a backward problem for a nonlinear time fractional wave equation in a bounded domain. By applying the properties of Mittag-Leffler functions and the method of eigenvalue expansion, we establish some results about the existence and uniqueness of the mild solutions of the proposed problem based on the compact technique. Due to the ill-posedness of backward problem in the sense of Hadamard, a general filter regularization method is utilized to approximate the solution and further we prove the convergence rate for the regularized solutions.

scholarly journals On the Fractional Wave Equation

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 874
Author(s):  
Francesco Iafrate ◽  
Enzo Orsingher
Keyword(s):  
Brownian Motion ◽  
Wave Equation ◽  
Wave Equations ◽  
Stable Process ◽  
Space Time ◽  
Probabilistic Interpretation ◽  
Symmetric Stable Process ◽  
Fractional Wave Equation ◽  
Fractional Wave Equations ◽  
Time Fractional Wave Equation

In this paper we study the time-fractional wave equation of order 1 < ν < 2 and give a probabilistic interpretation of its solution. In the case 0 < ν < 1 , d = 1 , the solution can be interpreted as a time-changed Brownian motion, while for 1 < ν < 2 it coincides with the density of a symmetric stable process of order 2 / ν . We give here an interpretation of the fractional wave equation for d > 1 in terms of laws of stable d−dimensional processes. We give a hint at the case of a fractional wave equation for ν > 2 and also at space-time fractional wave equations.

scholarly journals A novel semi-analytical method for solutions of two dimensional fuzzy fractional wave equation using natural transform

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Muhammad Arfan ◽  
Kamal Shah ◽  
Aman Ullah ◽  
Soheil Salahshour ◽  
Ali Ahmadian ◽  
...  
Keyword(s):  
Wave Equation ◽  
Analytical Method ◽  
Two Dimensional ◽  
Fractional Wave Equation
Sign in / Sign up

Export Citation Format

Share Document