Despite the fact the Laplace transform has an appreciable efficiency in solving many
equations, it cannot be employed to nonlinear equations of any type. This paper presents a …

A hybrid analytical technique for solving multi-dimensional time-fractional Navier-Stokes system
Page 1 AIMS Mathematics, 8(1): 1713–1736. DOI: 10.3934/math.2023088 Received: 16 August …

This article circumvents the Laplace transform to provide an analytical solution in a power
series form for singular, non-singular, linear, and non-linear ordinary differential equations. It …

The Laplace residual power series method was introduced as an effective technique for
finding exact and approximate series solutions to various kinds of differential equations. In …

Effective transform-expansions algorithm for solving non-linear fractional multi-pantograph
system Page 1 AIMS Mathematics, 8(9): 19950–19970. DOI: 10.3934/math.20231017 Received …

This paper aims to explore and examine a fractional differential equation in the fuzzy
conformable derivative sense. To achieve this goal, a novel analytical algorithm is …

This paper used the flexible and efficient least squares residual power series method
(LSRPSM) to solve the time-fractional derivative Cahn-Hilliard and Gardener equations. The …

The presented paper aims to investigate, examine, and analyze the nonlinear time-fractional
evolution partial differential equations (TFNE-PDEs) in the sense of Caputo essential in …

The time-fractional order differential equations are used in many different contexts to
analyse the integrated scientific phenomenon. Hence these equations are the point of …

The article focuses on finding analytical series solutions for linear and nonlinear partial
differential equations. It introduces a new technique named the limit residual function …