On dual q-Integral equations and some iterative methods based on q-di{uFB00}erence operators /
Ola Abdelnaby Ashour Abdelnaby
On dual q-Integral equations and some iterative methods based on q-dierence operators / الفرقية- qلتكاملية المترفقة وبعض الطرق التكرارية المعتمدة على المؤثرات -q حول العادلات Ola Abdelnaby Ashour Abdelnaby ; Supervised Alaa E. Hamza , Mourad E. H. Ismail - Cairo : Ola Abdelnaby Ashour Abdelnaby , 2015 - 106 P. ; 25cm
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- cic 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 dierent 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 Steensens method of fourth-order convergence is introduced
Dual q-integral equations Fractional q-integral operators The third Jackson q-Bessel function
On dual q-Integral equations and some iterative methods based on q-dierence operators / الفرقية- qلتكاملية المترفقة وبعض الطرق التكرارية المعتمدة على المؤثرات -q حول العادلات Ola Abdelnaby Ashour Abdelnaby ; Supervised Alaa E. Hamza , Mourad E. H. Ismail - Cairo : Ola Abdelnaby Ashour Abdelnaby , 2015 - 106 P. ; 25cm
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- cic 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 dierent 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 Steensens method of fourth-order convergence is introduced
Dual q-integral equations Fractional q-integral operators The third Jackson q-Bessel function