Introduction Integral transforms are important to solve real problems. Appropriate choice of
integral transforms helps to convert differential equations as well as integral equations into …

Laplace and Fourier transforms are widely used independently in engineering for linear
differential equations including fractional differential equations. Here we introduce a …

This article reviews the Adomian decomposition method (ADM) and its developments to
handle singular and non-singular initial, boundary value problems in ordinary and partial …

In this letter, we consider the new nonlinear Burgers' equation engaging local fractional
derivative for the first time. With the use of the travelling‐wave transformation of non …

In this paper, a hybrid local fractional technique is applied to some local fractional partial
differential equations. Partial differential equations modeled with local fractional derivatives …

This study proposes a new fractal modified equal width-Burgers equation (MEWBE) with the
local fractional derivative (LFD) for the first time. By defining the Mittag-Leffler function (MLF) …

In the present paper, we employ a wavelets optimization method is employed for the
elucidations of fractional partial differential equations of pricing European option …

A new local fractional modified Benjamin–Bona–Mahony equation is proposed within the
local fractional derivative in this study for the first time. By defining some elementary …

In this work, a general class of pantograph type nonlinear fractional integro-differential
equations (PT-FIDEs) with non-singular and non-local kernel is considered. A numerical …

The analytical approximate solutions of the wave equation with local fractional derivative
operators (LFDOs) are utilized in this manuscript. The reduced differential transform method …