| Summary: | In this paper, we introduce new three-point fractional formulas which represent three generalizations for the well-known classical three-point formulas; central, forward and backward formulas. This has enabled us to study the function’s behavior according to different fractional-order values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> numerically. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability.
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