New perspective on the conventional solutions of the nonlinear time‐fractional partial differential equations

H Ahmad, A Akgül, TA Khan, PS Stanimirović… - …, 2020 - Wiley Online Library
The role of integer and noninteger order partial differential equations (PDE) is essential in
applied sciences and engineering. Exact solutions of these equations are sometimes difficult …

Numerical investigation of fractional-order Swift–Hohenberg equations via a Novel transform

K Nonlaopon, AM Alsharif, AM Zidan, A Khan… - Symmetry, 2021 - mdpi.com
In this paper, the Elzaki transform decomposition method is implemented to solve the time-
fractional Swift–Hohenberg equations. The presented model is related to the temperature …

Approximate analytical solution of the nonlinear fractional KdV–Burgers equation: a new iterative algorithm

A El-Ajou, OA Arqub, S Momani - Journal of Computational Physics, 2015 - Elsevier
In this paper, explicit and approximate solutions of the nonlinear fractional KdV–Burgers
equation with time–space-fractional derivatives are presented and discussed. The solutions …

[HTML][HTML] The first integral method for some time fractional differential equations

B Lu - Journal of Mathematical Analysis and Applications, 2012 - Elsevier
In this paper, the fractional derivatives in the sense of modified Riemann–Liouville derivative
and the first integral method are employed for constructing the exact solutions of nonlinear …

[HTML][HTML] A new modified definition of Caputo–Fabrizio fractional-order derivative and their applications to the multi step homotopy analysis method (MHAM)

H Yépez-Martínez, JF Gómez-Aguilar - Journal of Computational and …, 2019 - Elsevier
In this paper, we present a new definition of fractional-order derivative with a smooth kernel
based on the Caputo–Fabrizio fractional-order operator which takes into account some …

The modified trial equation method for fractional wave equation and time fractional generalized Burgers equation

H Bulut, HM Baskonus, Y Pandir - Abstract and applied analysis, 2013 - Wiley Online Library
The fractional partial differential equations stand for natural phenomena all over the world
from science to engineering. When it comes to obtaining the solutions of these equations …

[HTML][HTML] On the modified (G′ G2)-expansion method for finding some analytical solutions of the traveling waves

S Behera, NH Aljahdaly, JPS Virdi - Journal of Ocean Engineering and …, 2022 - Elsevier
This work investigates three nonlinear equations that describe waves on the oceans which
are the Kadomtsev Petviashvili-modified equal width (KP-MEW) equation, the coupled …

A new analysis of fractional-order equal-width equations via novel techniques

M Naeem, AM Zidan, K Nonlaopon, MI Syam… - Symmetry, 2021 - mdpi.com
In this paper, the new iterative transform method and the homotopy perturbation transform
method was used to solve fractional-order Equal-Width equations with the help of Caputo …

[HTML][HTML] A fractional variational iteration method for solving fractional nonlinear differential equations

G Wu - Computers & Mathematics with Applications, 2011 - Elsevier
Recently, fractional differential equations have been investigated by employing the famous
variational iteration method. However, all the previous works avoid the fractional order term …

Series solutions of nonlinear conformable fractional KdV-Burgers equation with some applications

A El-Ajou, Z Al-Zhour, M Oqielat, S Momani… - The European Physical …, 2019 - Springer
In this paper, the non-linear fractional KdV-Burgers equation (KdVBE) in terms of
conformable fractional derivative (CFD) is reconstituted instead of the Caputo fractional …