Derivatives of noninteger order and their applications

Marek W. Michalski

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1993

Abstract

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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 &nbsp2. 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........................................................................................................................................451991 Mathematics Subject Classification: 26A33, 26B99, 34A99, 34B99, 35D99, 35L99, 45B05, 45D05, 45E10, 45Gxx, 45P05, 47Gxx.

How to cite

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Marek W. Michalski. Derivatives of noninteger order and their applications. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1993. <http://eudml.org/doc/268366>.

@book{MarekW1993,
abstract = {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 &nbsp2. 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........................................................................................................................................451991 Mathematics Subject Classification: 26A33, 26B99, 34A99, 34B99, 35D99, 35L99, 45B05, 45D05, 45E10, 45Gxx, 45P05, 47Gxx.},
author = {Marek W. Michalski},
keywords = {ordinary and partial nonlinear differential equations of fractional order; mixed Riemann-Liouville fractional integrals and derivatives; Abel integral equation; Mangeron polyvibrating equation; nonlinear integral equation},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Derivatives of noninteger order and their applications},
url = {http://eudml.org/doc/268366},
year = {1993},
}

TY - BOOK
AU - Marek W. Michalski
TI - Derivatives of noninteger order and their applications
PY - 1993
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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 &nbsp2. 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........................................................................................................................................451991 Mathematics Subject Classification: 26A33, 26B99, 34A99, 34B99, 35D99, 35L99, 45B05, 45D05, 45E10, 45Gxx, 45P05, 47Gxx.
LA - eng
KW - ordinary and partial nonlinear differential equations of fractional order; mixed Riemann-Liouville fractional integrals and derivatives; Abel integral equation; Mangeron polyvibrating equation; nonlinear integral equation
UR - http://eudml.org/doc/268366
ER -

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