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This article addresses the multiple composed Erde ́lyi-Kober fractional derivatives and integrals that are compositions of the suitable right- and left-sided Erde ́lyi-Kober derivatives and integrals. These operators are important, say, in the framework of the Euler-Lagrange equations in the fractional calculus of variations. We start with a discussion of their properties including inversion formulas, compositions, and mapping properties. Then, we introduce an integral transform of the Mellin convolution type related to the multiple composed Erde ́lyi-Kober integrals and derive some operational relations. Finally, a one parameter family of convolutions for the multiple composed Erde ́lyi-Kober integrals in the sense of Dimovski is constructed

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