ANALYTICAL APPROXIMATE SOLUTIONS OF TIME-FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS USING A NEW ITERATIVE TECHNIQUE

ANALYTICAL APPROXIMATE SOLUTIONS OF TIME-FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS USING A NEW ITERATIVE TECHNIQUE

M. Sadaf, G. Akram

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Abstract

In this manuscript, a new iterative technique is proposed to obtain the solu- tions of linear and nonlinear time-fractional integro-dierential equations. The suggested algorithm is a modication of the homotopy analysis method. The deformation equa- tions 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 dierent numerical test applications. The numerical and graphical results explicitly reveal the potential and accuracy of the proposed technique.

Keywords

Integro-dierential equations, Iterative Technique, Caputo fractional deriva- tive, Modied homotopy analysis method.