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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...

Elasticity is a fundamental property of all substances occurring in nature. The theory of elasticity is concerned with the study of the response of elastic bodies to the action of forces. The importance of the application of the theory of elasticity in physics and technical mechanics involved in the stated problems from the viewpoint of mathematical analysis attracted the attention of the greatest investigators of the 20th centuries to this branch of science. This thesis is devoted to study some problems in the mechanics of elastic bodies, which might have some interesting applications in the...