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In this short monograph Newton-like§and other similar numerical methods with applications to solving multivariate§equations are developed, which involve Caputo§type fractional mixed partial derivatives and multivariate fractional Riemann-Liouville§integral operators. These are studied for the first time in the literature. The§chapters are self-contained and can be read independently. An extensive list of§references is given per chapter. The book's results are expected to find§applications in many areas of applied mathematics, stochastics, computer§science and engineering. As such this short monograph is suitable for§researchers, graduate students, to be used in graduate classes and seminars of§the above subjects, also to be in all science and engineering libraries.§§