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In this work, some new results concerning orthogonality of some trigonometric and exponential functions with respect to special weight functions have been established. Moreover, the convergence of Nishimoto fractional differintegration under certain conditions has been found. New methods for solving some kinds of fractional differential, fractional integral and fractional integrodifferential equations are deduced. Finally, eigenvalues and eigenfunctions for special eigenvalue problems are studied Abstract
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