Investigation to analytic solutions of modified conformable time–space fractional mixed partial differential equations

Abstract

In this paper, the invariant subspace method (ISM) is developed to obtain the exact solution of linear and nonlinear time and space fractional mixed partial differential equations involving modified conformable fractional derivative (MCFD). Moreover, the method is successfully extended to the coupled system of modified conformable fractional differential equations. Variety of time-space fractional mixed PDEs are considered and solved to illustrate the established result of ISM. Finally, a comparison between exact solution of fractional PDE in the sense of MCFD and Caputo fractional derivative (Ca-FD) is presented through some examples of time–space fractional mixed partial differential equations.

Keywords

• Modified conformable fractional derivative
• Analytic solution
• Invariant subspace
• Fractional calculus
• Fractional partial differential equation