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Abel’s integral equation is an efficient singular integral equation that plays an important role in diverse fields of science. This paper aims to investigate Abel’s integral equation and its solution using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mi>α</mi></msub></semantics></math></inline-formula>-transform, which is a symmetric relation between Laplace and Sumudu transforms. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mi>α</mi></msub></semantics></math></inline-formula>-transform, as defined via distribution space, is employed to establish a solution to Abel’s integral equation, interpreted in the sense of distributions. As an application to the given theory, certain examples are given to demonstrate the efficiency and suitability of using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mi>α</mi></msub></semantics></math></inline-formula>-transform method in solving integral equations.