Titel: QUANTUM CALCULUS: NEW CONCEPTS, IMPULSIVE IVPS AND BVPS, INEQUALITIES (Trends in Abstract and Applied Analysis, 4)
Verlag: World Scientific Pub Co Inc
Erscheinungsjahr: 2016
Sprache: Englisch
ISBN-10: 9813141522
ISBN-13: 9789813141520
Einband: Hardcover
Zustand: New

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Inhaltsangabe

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 q_k-derivative and q_k-integral, and establish their basic properties. As applications, we study initial and boundary value problems of impulsive q_k-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 q_k-calculus. In the second part, we develop fractional quantum calculus in relation to a new q_k-shifting operator and establish some existence and q_k uniqueness results for initial and boundary value problems of impulsive fractional q_k-difference equations.

�ber die Autorin bzw. den Autor

Charlotte y Peter Fiell son dos autoridades en historia, teor�a y cr�tica del dise�o y han escrito m�s de sesenta libros sobre la materia, muchos de los cuales se han convertido en �xitos de ventas. Tambi�n han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Dise�o del siglo XX, El dise�o industrial de la A a la Z, Scandinavian Design y Dise�o del siglo XXI.

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