Thesis (Ph.D.) - Cairo University - Faculty of Science - Department of Mathematics

This work is mainly concerned with solving dual q-integral equations, dual and triple sequence equations, and dual series equations with spe- ci{uFB01}c choices for the kernel function in each case. An extensive study of dual q-integral equations when the kernel is the third Jackson q-Bessel function is introduced. There are di{uFB00}erent approaches for solving dual integral equations when the kernel is a Bessel function like the multi- plying factor method, and the fractional calculus approach. There is also the Mellin transform approach which is used to convert the system to a Fredholm integral equation of the second kind that can be solved numerically. An extensive account for these approaches is in the book of Sneddon (1966). q-analogues of these approaches are introduced and used to solve or convert system of q-dual integral equations into Fredholm q-integral equations of the second kind. A dual and triple se- quence equations when the kernel is q-orthogonal polynomials is solved and examples are included. Also, a dual series equation involving the q-Laguerre polynomials as a kernel is solved. Finally, A q-variant of Ste{uFB00}ensen{u2019}s method of fourth-order convergence is introduced

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