Quantum Calculus: New Concepts, Impulsive Ivps And Bvps, Inequalities
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A01=Bashir Ahmad
A01=Jessada Tariboon
A01=Sotiris K Ntouyas
Author_Bashir Ahmad
Author_Jessada Tariboon
Author_Sotiris K Ntouyas
Category=PBKA
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Existence
Fixed Point Theorems
Fractional Integral Inequalities
Hybrid Differential Equations
Impulsive Fractional qk-difference Equations
Langevin Equation
Quantum Calculus
Uniqueness
Product details
- ISBN 9789813141520
- Publication Date: 28 Jul 2016
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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The main objective of this book is to extend the scope of the q-calculus based on the definition of q-derivative [Jackson (1910)] to make it applicable to dense domains. As a matter of fact, Jackson's definition of q-derivative fails to work for impulse points while this situation does not arise for impulsive equations on q-time scales as the domains consist of isolated points covering the case of consecutive points. In precise terms, we study quantum calculus on finite intervals.In the first part, we discuss the concepts of qk-derivative and qk-integral, and establish their basic properties. As applications, we study initial and boundary value problems of impulsive qk-difference equations and inclusions equipped with different kinds of boundary conditions. We also transform some classical integral inequalities and develop some new integral inequalities for convex functions in the context of qk-calculus. In the second part, we develop fractional quantum calculus in relation to a new qk-shifting operator and establish some existence and qk uniqueness results for initial and boundary value problems of impulsive fractional qk-difference equations.
