Fractional Differentiation InequalitiesIn this book the author presents the Opial, Poincaré, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for the above are derived using three different types of fractional derivatives, namely by Canavati, Riemann-Liouville and Caputo. The univariate and multivariate cases are both examined. Each chapter is self-contained. The theory is presented systematically along with the applications. The application to information theory is also examined. This monograph is suitable for researchers and graduate students in pure mathematics. Applied mathematicians, engineers, and other applied scientists will also find this book useful. |
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Table des matières
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| 48 | |
| 53 | |
| 56 | |
| 66 | |
| 69 | |
| 72 | |
| 96 | |
| 107 | |
| 108 | |
| 109 | |
XXVI | 138 |
XXVII | 149 |
XXVIII | 150 |
XXIX | 152 |
XXX | 169 |
XXXI | 178 |
XXXII | 180 |
XXXIII | 181 |
XXXIV | 195 |
XXXV | 205 |
XXXVI | 206 |
XXXVII | 209 |
XXXVIII | 220 |
XXXIX | 228 |
XL | 230 |
XLI | 231 |
XLII | 244 |
XLIII | 251 |
XLIV | 257 |
XLV | 258 |
XLVI | 269 |
XLVII | 270 |
XLVIII | 279 |
XLIX | 280 |
L | 318 |
LI | 320 |
LII | 323 |
LXI | 411 |
LXII | 419 |
LXIII | 424 |
LXIV | 427 |
LXV | 431 |
LXVI | 436 |
LXVII | 445 |
LXVIII | 446 |
LXIX | 457 |
LXX | 473 |
LXXI | 479 |
LXXII | 483 |
LXXIII | 484 |
LXXIV | 503 |
LXXV | 505 |
LXXVI | 506 |
LXXVII | 523 |
LXXVIII | 524 |
LXXIX | 527 |
LXXX | 545 |
LXXXI | 550 |
LXXXII | 553 |
LXXXIII | 563 |
LXXXIV | 568 |
LXXXV | 577 |
LXXXVI | 581 |
LXXXVII | 588 |
LXXXVIII | 591 |
LXXXIX | 595 |
XC | 598 |
XCI | 615 |
XCII | 618 |
XCIII | 622 |
XCIV | 634 |
XCV | 638 |
XCVI | 641 |
XCVII | 671 |
XCVIII | 673 |
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Expressions et termes fréquents
_ffere absolutely continuous AQ+i Assume f G assumptions Based on Theorem Canavati fractional Caputo fractional derivative continue with Theorem continuous functions D"af define Denote derivative D@f drv dx Dvaf exists f G ACn fixed sign a.e. fractional calculus fractional differential equations fractional integral Fubini's theorem Further assume G AC G Loo G R+ G.A. Anastassiou gamma function give Corollary give Theorem Hence Holder's inequality holds initial value problem integrable fractional derivative Lebesgue integrable Lebesgue measurable Lemma Let f G multi-index multivariate need Theorem obtain Opial partial derivatives proof of Theorem Proposition proving the claim Riemann Riemann-Liouville fractional derivative Similar to Theorem spherical shell Springer Science+Business Media Taylor formula TTien Vx G Ziaue λ α λ β λ ν λα λβ λν
Informations bibliographiques
| Titre | Fractional Differentiation Inequalities Mathematics and Statistics |
| Auteur | George A. Anastassiou |
| Édition | illustrée |
| Éditeur | Springer Science & Business Media, 2009 |
| ISBN | 0387981284, 9780387981284 |
| Longueur | 686 pages |
| Exporter la citation | BiBTeX EndNote RefMan |