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Quantum calculus: new concepts, impulsive ivps and bvps, inequalities

By: Contributor(s): Material type: TextTextSeries: Trends in abstract and applied analysis; Vol. 4Publication details: New Jersey World Scientific 2016Description: xii, 276 pISBN:
  • 9789813141520
Subject(s): DDC classification:
  • 515 A4Q8
Summary: 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. http://www.worldscientific.com/worldscibooks/10.1142/10075
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Item type Current library Item location Collection Shelving location Call number Status Date due Barcode
Books Vikram Sarabhai Library Rack 28-A / Slot 1370 (0 Floor, East Wing) Non-fiction General Stacks 515 A4Q8 (Browse shelf(Opens below)) Available 192899

1.Preliminaries
2.Quantum Calculus on Finite Intervals
3.Initial Value Problems for Impulsive qk-Difference Equations and Inclusions
4.Boundary Value Problems for First-Order Impulsive qk-Integro-Difference Equations and Inclusions
5.Impulsive qk-Difference Equations with Different Kinds of Boundary Conditions
6.Nonlinear Second-Order Impulsive qk-Difference Langevin Equation with Boundary Conditions
7.Quantum Integral Inequalities on Finite Intervals
8.Impulsive Quantum Difference Systems with Boundary Conditions
9.New Concepts of Fractional Quantum Calculus and Applications to Impulsive Fractional qk-Difference Equations
10.Integral Inequalities via Fractional Quantum Calculus
11.Nonlocal Boundary Value Problems for Impulsive Fractional qk-Difference Equations
12.Existence Results for Impulsive Fractional qk-Difference Equations with Anti-periodic Boundary Conditions
13.Impulsive Fractional qk-Integro-Difference Equations with Boundary Conditions
14.Impulsive Hybrid Fractional Quantum Difference Equations

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.

http://www.worldscientific.com/worldscibooks/10.1142/10075

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