الفهرس 
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Abstract
The main objective of this thesis is to discuss in details the different properties of the generalized Hankel transforms (GHT) and introducing the GHT of new differentiable operators. Also, GHT method is used for obtaining exact solutions to some PDEs of practical importance. The thesis is organized in five chapters. Chapter one gives a brief introduction to the concept of the integral transforms including many well known transforms and some problems that are amenable to be solved using these transforms. Chapter two is concerned with the operational calculus of Hankel transforms (HT) with illustrative examples. Chapter three is devoted to operational calculus of GHT and deriving the GHT of new differential operators which appear in many PDEs. In chapter four the problem of pollutants transport into the atmosphere is considered and closed form solutions are obtained in terms of known functions. In addition, we discuss the effect of the problem parameters on the pollutant concentrations at different levels. Chapter five completes this thesis where we introduce some conclusion remarks on the obtained results in chapters three and four. Also, suggestions for a future work are stated. To ensure that the thesis is selfcontained, we added two appendices. The first summaries some special functions and their properties and the second displays some useful integrals involving Bessel functions.