q-Fractional Calculus and Equations

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Science, Physics, Mathematical Physics
Cover of the book q-Fractional Calculus and Equations by Mahmoud H. Annaby, Zeinab S. Mansour, Springer Berlin Heidelberg
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Mahmoud H. Annaby, Zeinab S. Mansour ISBN: 9783642308987
Publisher: Springer Berlin Heidelberg Publication: August 27, 2012
Imprint: Springer Language: English
Author: Mahmoud H. Annaby, Zeinab S. Mansour
ISBN: 9783642308987
Publisher: Springer Berlin Heidelberg
Publication: August 27, 2012
Imprint: Springer
Language: English

This nine-chapter monograph introduces a rigorous investigation of *q-*difference operators in standard and fractional settings. It starts with elementary calculus of *q-*differences and integration of Jackson’s type before turning to *q-*difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular  *q-*Sturm–Liouville theory is also introduced; Green’s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi. Hence fractional *q-*calculi of the types Riemann–Liouville; Grünwald–Letnikov;  Caputo;  Erdélyi–Kober and Weyl are defined analytically. Fractional *q-*Leibniz rules with applications  in *q-*series are  also obtained with rigorous proofs of the formal  results of  Al-Salam-Verma, which remained unproved for decades. In working towards the investigation of *q-*fractional difference equations; families of *q-*Mittag-Leffler functions are defined and their properties are investigated, especially the *q-*Mellin–Barnes integral  and Hankel contour integral representation of  the *q-*Mittag-Leffler functions under consideration,  the distribution, asymptotic and reality of their zeros, establishing *q-*counterparts of Wiman’s results. Fractional *q-*difference equations are studied; existence and uniqueness theorems are given and classes of Cauchy-type problems are completely solved in terms of families of *q-*Mittag-Leffler functions. Among many *q-*analogs of classical results and concepts, *q-*Laplace, *q-Mellin and q2-*Fourier transforms are studied and their applications are investigated.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This nine-chapter monograph introduces a rigorous investigation of *q-*difference operators in standard and fractional settings. It starts with elementary calculus of *q-*differences and integration of Jackson’s type before turning to *q-*difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular  *q-*Sturm–Liouville theory is also introduced; Green’s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi. Hence fractional *q-*calculi of the types Riemann–Liouville; Grünwald–Letnikov;  Caputo;  Erdélyi–Kober and Weyl are defined analytically. Fractional *q-*Leibniz rules with applications  in *q-*series are  also obtained with rigorous proofs of the formal  results of  Al-Salam-Verma, which remained unproved for decades. In working towards the investigation of *q-*fractional difference equations; families of *q-*Mittag-Leffler functions are defined and their properties are investigated, especially the *q-*Mellin–Barnes integral  and Hankel contour integral representation of  the *q-*Mittag-Leffler functions under consideration,  the distribution, asymptotic and reality of their zeros, establishing *q-*counterparts of Wiman’s results. Fractional *q-*difference equations are studied; existence and uniqueness theorems are given and classes of Cauchy-type problems are completely solved in terms of families of *q-*Mittag-Leffler functions. Among many *q-*analogs of classical results and concepts, *q-*Laplace, *q-Mellin and q2-*Fourier transforms are studied and their applications are investigated.

More books from Springer Berlin Heidelberg

Cover of the book Data Management and Query Processing in Semantic Web Databases by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book Die unerklärliche Müdigkeit by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book Linear Algebra for Economists by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book Formal Grammar by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book ISO Standards for Geographic Information by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book Proceedings of the FISITA 2012 World Automotive Congress by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book From Publishing to Knowledge Networks by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book Indoor Air Quality by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book Nonabelian Jacobian of Projective Surfaces by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book Dem Computer ins Hirn geschaut by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book Surviving Intensive Care by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book Andrology by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book JIMD Reports, Volume 31 by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book eHealth in Deutschland by Mahmoud H. Annaby, Zeinab S. Mansour
Cover of the book Frontiers in European Radiology by Mahmoud H. Annaby, Zeinab S. Mansour
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy