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Purpose

This paper aims to directly extend the homotopy perturbation method to study the coupled Burgers equations with time‐ and space‐fractional derivatives.

Design/methodology/approach

The realistic numerical solutions were obtained in a form of rapidly convergent series with easily computable components.

Findings

The figures show the effectiveness and good accuracy of the proposed method.

Originality/value

The paper obtains realistic numerical solutions in a form of rapidly convergent series with easily computable components. It shows the effectiveness and good accuracy of the proposed method.

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