Derivatives of noninteger order and their applications

Marek W. Michalski

GDML_Books, (1993), p.

Résumé

CONTENTS  Introduction........................................................................................................................................5I. Derivatives of noninteger order.........................................................................................................6II. Characteristic problem for the Mangeron polyvibrating equation of noninteger order....................17  1. The problem................................................................................................................................17  2. Existence of solutions..................................................................................................................18  3. Uniqueness of the solution...........................................................................................................21  4. Continuous solutions...................................................................................................................23  5. Continuous dependence of the solution on the boundary data...................................................25III. Noncharacteristic boundary value problem...................................................................................26  1. The problem................................................................................................................................26  2. Local solutions of the problem.....................................................................................................27  3. Extension of the local solution.....................................................................................................30IV. Some problems for ordinary differential equations........................................................................32  1. Multipoint problem.......................................................................................................................32    ;1.1. The problem..........................................................................................................................32    ;1.2. Solution of the problem.........................................................................................................33  2. Polarographic equation...............................................................................................................35    ;2.1. The Cauchy problem.............................................................................................................35    ;2.2. Continuous dependence of the solution on the initial data....................................................39    ;2.3. The multipoint problem..........................................................................................................39V. Further applications of the derivatives of noninteger order...........................................................40  1. An application to Mikusi/nski's operator theory............................................................................40  2. Integral representation of analytic functions................................................................................42References........................................................................................................................................45

1991 Mathematics Subject Classification: 26A33, 26B99, 34A99, 34B99, 35D99, 35L99, 45B05, 45D05, 45E10, 45Gxx, 45P05, 47Gxx.

Détail

Zbl 0880.26007

EUDML-ID : urn:eudml:doc:268366