The subjects of special functions of single complex variable and several complex variables have a great situation in almost all disciplines Mathematics, Physics and Engineering. The present work is devoted to study these subjects and is considered one of several theses, which were presented and are still presenting by the school established by Sayyed in one of the branches of complex analysis. This thesis is divided into six main chapters. The main aim of Chapter 1 is to define a new family of special functions, say, $p$-Bessel function of one complex variable. The aim of Chapter 2 is to...