A reliable method for the space-time fractional Burgers and time-fractional Cahn-Allen equations via the FRDTM

DOI10.1186/s13662-017-1148-8zbMath1422.35170OpenAlexW2598853220WikidataQ59518376 ScholiaQ59518376MaRDI QIDQ1628659

Mahmoud S. Rawashdeh

Publication date: 4 December 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-017-1148-8

zbMATH Keywords

Burgers equationsCaputo fractional derivativeCahn-Allen equationfractional reduced differential transform method

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Fractional derivatives and integrals (26A33) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Theoretical approximation in context of PDEs (35A35) Numerical methods for initial value problems involving ordinary differential equations (65L05) Fractional partial differential equations (35R11)

Related Items

An approximation to the solution of time fractional modified Burgers' equation using extended cubic B-spline method, Time-fractional Cahn-Allen and time-fractional Klein-Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis, Modified fractional reduced differential transform method for the solution of multiterm time-fractional diffusion equations, Numerical approach for time-fractional Burgers' equation via a combination of Adams-Moulton and linearized technique, Theories and applications of the inverse fractional natural transform method, Analysis and numerical simulation of fractional order Cahn-Allen model with Atangana-Baleanu derivative, Approximate analytical solution of one-dimensional beam equations by using time-fractional reduced differential transform method, Global unsolvability of the Burgers equation with fractional time derivative, Applications of fractional reduced differential transform method for solving the generalized fractional-order FitzHugh-Nagumo equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new algorithm for solving dynamic equations on a time scale
• Numerical solutions for systems of nonlinear fractional ordinary differential equations using the FNDM
• An efficient approach for fractional Harry Dym equation by using Sumudu transform
• Thermoelasticity of initially stressed bodies, asymptotic equipartition of energies
• A new numerical technique for solving the local fractional diffusion equation: two-dimensional extended differential transform approach
• A domain of influence theorem for microstretch elastic materials
• Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation
• The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• On solutions of fractional Riccati differential equations
• Approximate analytical solution for seepage flow with fractional derivatives in porous media
• Fractional telegraph equations.
• A generalized differential transform method for linear partial differential equations of fractional order
• Generalized differential transform method: Application to differential equations of fractional order
• Non-perturbative analytical solutions of the space- and time-fractional Burgers equations
• An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method
• Solution of an extraordinary differential equation by Adomian decomposition method
• Analytic and approximate solutions of the space- and time-fractional telegraph equations
• Numerical solutions of time‐fractional Burgers equations
• Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method