q -Fractional Calculus and Equations

• Main Authors: Annaby, Mahmoud H. (Author), Mansour, Zeinab S. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.
• Series: Lecture Notes in Mathematics, 2056
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Difference equations.; Functional equations.; Functions of complex variables.; Integral equations.; Integral transforms.; Operational calculus.; Physics.; Analysis.; Difference and Functional Equations.; Functions of a Complex Variable.; Integral Transforms, Operational Calculus.; Integral Equations.; Mathematical Methods in Physics.

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 der...

Table of Contents:

• 1 Preliminaries
• 2 q-Difference Equations
• 3 q-Sturm Liouville Problems
• 4 Riemann–Liouville q-Fractional Calculi
• 5 Other q-Fractional Calculi
• 6 Fractional q-Leibniz Rule and Applications
• 7 q-Mittag–Leffler Functions
• 8 Fractional q-Difference Equations
• 9 Applications of q-Integral Transforms.