Abstract
In this paper, we introduce a generalized Mellin transform in the framework of fractional operators with respect to functions. The generalized Mellin transform is derived form the generalized Fourier transform with respect to functions. We prove several fundamental properties of the generalized Mellin transform. Relation of the generalized Mellin transform with various fractional calculus operators is investigated. Generalized Mellin convolutions are defined and applied for solution of a certain differential equation.

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We are very grateful to the anonymous reviewers for their useful comments that led to improvement of the manuscript.
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Communicated by Roberto Garrappa.
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Aziz, T., Rehman, M.u. Generalized Mellin transform and its applications in fractional calculus. Comp. Appl. Math. 41, 88 (2022). https://doi.org/10.1007/s40314-022-01802-9
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DOI: https://doi.org/10.1007/s40314-022-01802-9