Fractional Differential Operators and Generalized Oscillatory Dynamics

Rami Ahmad El-Nabulsi

Abstract


In this paper, a new generalized fractional derivative is introduced holding many important properties. By implementing this new definition inside the Lagrangian $L: \mathcal{TQ}\to {\mathbb R}$, where $\mathcal{Q}$ is an $n$-dimensional manifold and $\mathcal{TQ}$ its tangent bundle, the new definition was used to discuss many interesting and general properties of the Lagrangian and Hamiltonian formalisms starting from a fractional actionlike variational approach. Applications of the new formalism for solving some dynamical oscillatory models of fractional order are given. Additional attractive features are explored in some details.

Full Text: PDF

Refbacks

  • There are currently no refbacks.


The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

Copyright 2020 by the Mathematical Association of Thailand.

All rights reserve. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the Mathematical Association of Thailand.

|ISSN 1686-0209|