Quantum Calculus : New Concepts, Impulsive IVPs and BVPs, Inequalities

Ahmad, Bashir; Ntouyas, Sotiris; Tariboon, Jessada

ISBN 10: 9813141522 / ISBN 13: 9789813141520

Editore: World Scientific Pub Co Inc, 2016

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Dati bibliografici

• Titolo: Quantum Calculus : New Concepts, Impulsive IVPs and BVPs, Inequalities
• Editore: World Scientific Pub Co Inc
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 9813141522
• ISBN 13: 9789813141520
• Rilegatura: Rilegato
• Condizione: As New

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Riassunto

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 q-shifting operator and establish some existence and uniqueness results for initial and boundary value problems of impulsive fractional q-difference equations.