Analytical approximate solutions of time-fractional integro-differential equations using a new iterative technique

In this manuscript, a new iterative technique is proposed to obtain the solutions of linear and nonlinear time-fractional integro-differential equations. The suggested algorithm is a modification of the homotopy analysis method. The deformation equations obtained in this case are easily integrable and the calculations involved in the algorithm are much simpler than the standard homotopy analysis method. The method is illustrated with the help of different numerical test applications. The numerical and graphical results explicitly reveal the potential and accuracy of the proposed technique.Publisher's Versio

Residual Power Series Method for Solving Time-fractional Model of Vibration Equation of Large Membranes

The primary aim of this manuscript is to present the approximate analytical solutions of the time fractional order α (

An operator-based approach for the construction of closed-form solutions to fractional differential equations

An operator-based approach for the construction of closed-form solutions to fractional differential equations is presented in this paper. The technique is based on the analysis of Caputo and Riemann-Liouville algebras of fractional power series. Explicit solutions to a class of linear fractional differential equations are obtained in terms of Mittag-Leffler and fractionally-integrated exponential functions in order to demonstrate the viability of the proposed technique