A semi-linear delayed diffusion-wave system with distributed order in time

Theoretical Analysis (Convergence and Stability) of a Difference Approximation for Multiterm Time Fractional Convection Diffusion-Wave Equations with Delay

“…The existence and uniqueness of the global mild solutions for the problem of nonlinear fractional reaction-diffusion equations with delay and Caputo's fractional derivatives are addressed in [6]. This work can be considered to be an extension of our previously published work [7], in which we discussed a single term time fractional wave equation with spatial constant coefficients. The scheme was of 2 − α order in time and fourth in space.…”

A general framework for the numerical analysis of high-order finite difference solvers for nonlinear multi-term time-space fractional partial differential equations with time delay

“…Based on the L1 formula on nonuniform meshes for time stepping and the Legendre-Galerkin spectral method for space discretization, a fully discrete numerical scheme is constructed. In [9], a numerical scheme based on a linearized compact difference scheme for a class of non-linear distributed order fractional diffusion-wave equations with fixed time-delay is considered. The focus lies on the derivation of the scheme as well as on quantitatively analyzing it theoretically.…”

On the applicability of Genocchi wavelet method for different kinds of fractional‐order differential equations with delay

“…Hosseinpour et al used Müntz‐Legendre polynomials for delay time‐fractional partial differential equations. For additional information, see other works …”

“…For additional information, see other works. [36][37][38] During the 1980s, wavelet analysis due to their successful application in signal and image processing became famous in various branches of science. In addition, characteristics such as orthogonality, arbitrary regularity, and good localization of wavelets have attracted many scientists.…”