Fractional differential equations, compatibility, and exact solutions

Lie symmetry analysis, invariant subspace method and q-homotopy analysis method for solving fractional system of single-walled carbon nanotube

(2021) Xiaoyu Cheng et al.   COMPUTATIONAL & APPLIED MATHEMATICS

New Explicit Solutions to the Fractional-Order Burgers’ Equation

(2021) M. Hafiz Uddin et al.   MATHEMATICAL PROBLEMS IN ENGINEERING

Explicit wave phenomena to the couple type fractional order nonlinear evolution equations

(2021) M. Ayesha Khatun et al.   Results in Physics

Abundant new exact solutions to the fractional nonlinear evolution equation via Riemann-Liouville derivative

(2021) M. Hafiz Uddin et al.   Alexandria Engineering Journal

A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions

(2020) Gangwei Wang et al.   NUCLEAR PHYSICS B

Fractional generalised homotopy analysis method for solving nonlinear fractional differential equations

(2020) S. R. Saratha et al.   computational and applied mathematics

Nonclassical symmetries and analytic solutions to Kawahara equation

(2020) Pallavi Verma et al.   INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS

Lie symmetry analysis, conservation laws and separation variable type solutions of the time-fractional porous medium equation

(2020) Ying Yang et al.   Waves in Random and Complex Media

Lie symmetry analysis for obtaining the abundant exact solutions, optimal system and dynamics of solitons for a higher-dimensional Fokas equation

(2020) Sachin Kumar et al.   CHAOS SOLITONS & FRACTALS

Analysis of Lie symmetries with conservation laws and solutions for the generalized (3+1)-dimensional time fractional Camassa–Holm–Kadomtsev–Petviashvili equation

(2019) Changna Lu et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

A piecewise spectral-collocation method for solving fractional Riccati differential equation in large domains

(2019) H. Azin et al.   computational and applied mathematics

An efficient numerical method for variable order fractional functional differential equation

(2018) Jiabao Yang et al.   APPLIED MATHEMATICS LETTERS

Exact and numerical solutions of time-fractional advection–diffusion equation with a nonlinear source term by means of the Lie symmetries

(2018) Alessandra Jannelli et al.   NONLINEAR DYNAMICS

Lie symmetry analysis, conservation laws and analytical solutions of the time-fractional thin-film equation

(2018) Xiu-Bin Wang et al.   COMPUTATIONAL & APPLIED MATHEMATICS

A (2+1)-dimensional KdV equation and mKdV equation: Symmetries, group invariant solutions and conservation laws

(2018) Gangwei Wang et al.   PHYSICS LETTERS A

Lie symmetry analysis of steady-state fractional reaction-convection-diffusion equation

(2017) M.S. Hashemi et al.   OPTIK

Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations

(2017) S. Sabermahani et al.   computational and applied mathematics

Symmetry analysis and rogue wave solutions for the (2+1)-dimensional nonlinear Schrödinger equation with variable coefficients

(2016) Gangwei Wang   APPLIED MATHEMATICS LETTERS

Modified iteration method for solving fractional gas dynamics equation

(2016) Ramin Najafi et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Classical and nonclassical Lie symmetry analysis to a class of nonlinear time-fractional differential equations

(2016) R. Najafi et al.   NONLINEAR DYNAMICS

Nonclassical symmetries and similarity solutions of variable coefficient coupled KdV system using compatibility method

(2016) R. K. Gupta et al.   NONLINEAR DYNAMICS

Classical and nonclassical symmetry classifications of nonlinear wave equation with dissipation

(2015) Yinshan Yun et al.   APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION

Nonclassical analysis of the nonlinear Kompaneets equation

(2012) George W. Bluman et al.   JOURNAL OF ENGINEERING MATHEMATICS

Laplace’s transform of fractional order via the Mittag–Leffler function and modified Riemann–Liouville derivative

(2009) Guy Jumarie   APPLIED MATHEMATICS LETTERS