Quantum Calculus: New Concepts, Impulsive Ivps And Bvps, Inequalities
New Concepts, Impulsive IVPs and BVPs, Inequalities

 USD 37.99

 USD 37.99
Descripción de editorial
The main objective of this book is to extend the scope of the qcalculus based on the definition of qderivative [Jackson (1910)] to make it applicable to dense domains. As a matter of fact, Jackson's definition of qderivative fails to work for impulse points while this situation does not arise for impulsive equations on qtime 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 qkderivative and qkintegral, and establish their basic properties. As applications, we study initial and boundary value problems of impulsive qkdifference 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 qkcalculus. In the second part, we develop fractional quantum calculus in relation to a new qkshifting operator and establish some existence and qk uniqueness results for initial and boundary value problems of impulsive fractional qkdifference equations.
Contents:PreliminariesQuantum Calculus on Finite IntervalsInitial Value Problems for Impulsive qkDifference Equations and InclusionsBoundary Value Problems for FirstOrder Impulsive qkIntegroDifference Equations and InclusionsImpulsive qkDifference Equations with Different Kinds of Boundary ConditionsNonlinear SecondOrder Impulsive qkDifference Langevin Equation with Boundary ConditionsQuantum Integral Inequalities on Finite IntervalsImpulsive Quantum Difference Systems with Boundary ConditionsNew Concepts of Fractional Quantum Calculus and Applications to Impulsive Fractional qkDifference EquationsIntegral Inequalities via Fractional Quantum CalculusNonlocal Boundary Value Problems for Impulsive Fractional qkDifference EquationsExistence Results for Impulsive Fractional qkDifference Equations with Antiperiodic Boundary ConditionsImpulsive Fractional qkIntegroDifference Equations with Boundary ConditionsImpulsive Hybrid Fractional Quantum Difference Equations
Readership: Mathematics and physics researchers.
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