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In this book, generalization in the form of extension of special functions has been made with their properties and various applications. The new extension of the classical beta function is analyzed on the basis of numerical results, which are established by using MATLAB software. Also, by implementing new extended beta functions into hypergeometric functions. \newline In this work, this is the best endeavor towards the proposed. Formulas associated with generating relations, extensions of special functions. The properties of extended functions have been introduced and applied in fractional calculus for extended fractional operators. All the results are general in nature and by assigning the different values to the parameters numerous new and known results have shown in their special functions