Abstract:
Generalization of integral-differential Riemann–Liouville operator on the matrix order is reviewed and its properties are studied. Theorem of the composition of operators of the matrix of integration and differentiation can be proved. The necessary and sufficient conditions for the unique solvability of the matrix Abel equation in a special class of functions are obtained.
Keywords:fractional calculus, integro-differential operator of Riemann–Liouville, functions of matrices, matrix operator, system of Abel integral equations.
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