In this work, we discuss a fractional model of a flow equation in a simple pipeline. Pipeline narrowing is a crucial aspect in drinking water distribution processes, sewage system and in oil-well schemes. The solution of the mathematical model is determined with the aid of the Sumudu transform and finite Hankel transform. The results derived in the current study are in compact and graceful forms in terms of the Mittag-Leffler type function, which are convenient for numerical and theoretical evaluation.
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