Mellin transform analysis and integration by parts for Hadamard-type fractional integrals

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The mellin integral transform in fractional calculus (2013, methodology): “[2], [3], [5], [15], [20], [28], [30], [32], and [35].”
On Hadamard fractional integro-differential boundary value problems (2015, background): “Details and properties of Hadamard fractional derivative and integral can be found in [2,15–19].”
A NEW APPROACH TO GENERALIZED FRACTIONAL DERIVATIVES (2011, methodology): “, investigate properties of Hadamard fractional integral and deriva tive [1, 2, 3, 9, 11, 12, 14, 17].”
Initial-value problems for hybrid Hadamard fractional differential equations (2014, background): “A detailed description of Hadamard fractional derivative and integral can be found in [1, 5, 6, 7, 15, 16, 17].”
An Existence Theorem for Fractional Hybrid Differential Inclusions of Hadamard Type with Dirichlet Boundary Conditions (2014, background): “A detailed description of Hadamard fractional derivative and integral can be found in [2, 21, 22, 23, 24, 25].”
New fractional integral unifying six existing fractional integrals (2016, background): “Recent results about the Hadamard and Hadamard-type integrals such as Hadamard-type fractional calculus [21], composition and semigroup properties [7], Mellin transforms [6], integration by parts formulae [8], Gtransform representations [22], impulsive differential equations with Hadamard fractional”