Results 41 to 50 of about 161,465 (191)

Kolmogorov type inequalities for the Marchaud fractional derivatives on the real line and the half-line [PDF]

, 2014
In this paper we establish some new Kolmogorov type inequalities for the Marchaud and Hadamard fractional derivatives of functions defined on a real axis or semi-axis.
Babenko, V. F., Churilova, M. S., Parfinovych, N. V., Skorokhodov, D. S.   +3 more
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Lyapunov-type inequalities for fractional differential equations: a survey [PDF]

Surveys in Mathematics and its Applications, 2021
A survey of results on Lyapunov-type inequalities for fractional differential equations associated with a variety of boundary conditions is presented.
Sotiris K. Ntouyas, Bashir Ahmad
doaj  

A New Mixed Fractional Derivative with Applications in Computational Biology

Computation
This study develops a new definition of a fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels.
Khalid Hattaf
doaj   +1 more source

Cosmological Models with Fractional Derivatives and Fractional Action Functional [PDF]

, 2010
Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed.
A.R. El-Nabulsi, A.R. El-Nabulsi, A.R. El-Nabulsi, A.R. El-Nabulsi, A.R. El-Nabulsi, A.R. El-Nabulsi, A.R. El-Nabulsi, A.R. El-Nabulsi, A.R. El-Nabulsi, A.R. El-Nabulsi, C. Kiefer, D. Baleanu, D. Baleanu, G.S.F. Frederico, G.S.F. Frederico, I. Podlubny, J. Munkhammar, J.W. Norbury, M.D. Roberts, M.F. Li, S. Pelmutter, S.I. Vacaru, V. Sahni, V.K Shchigolev, V.K. Shchigolev, V.V. Kiselev, V.V. Uchaikin   +26 more
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On Fractional and Fractal Derivatives in Relation to the Physics of Fractals

Recoletos Multidisciplinary Research Journal, 2013
Fractional and fractal derivatives are both generalizations of the usual derivatives that consider derivatives of non-integer orders. Interest in these generalizations has been triggered by a resurgence of clamor to develop a mathematical tool to ...
Roberto N. Padua, Miraluna L. Herrera, Adriano V. Patac Jr., Michael V. Sabugaa, Gibson T. Maglasang, Mark S. Borres, Jay M. Ontolan   +6 more
doaj   +1 more source

Inequalities for Riemann–Liouville-Type Fractional Derivatives of Convex Lyapunov Functions and Applications to Stability Theory

Mathematics, 2023
In recent years, various qualitative investigations of the properties of differential equations with different types of generalizations of Riemann–Liouville fractional derivatives were studied and stability properties were investigated, usually using ...
Ravi P. Agarwal, Snezhana Hristova, Donal O’Regan   +2 more
doaj   +1 more source

Extending the D'Alembert Solution to Space-Time Modified Riemann-Liouville Fractional Wave Equations

, 2012
In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC.
-Sheng Duan, Baleanu, Bollini, Calcagni, Cresus F.L. Godinho, Fadeev, Goldfain, Guelfand, Herrmann, Hohenberg, Horava, Hornreich, J. Weberszpil, J.A. Helayël-Neto, Jumarie, Jumarie, Lifshitz, Ma, Metzler, Miller, Nobre, Nottale, Nottale, Plyushchay, Raspini, Weinberg   +25 more
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Non-local fractional derivatives. Discrete and continuous [PDF]

, 2016
We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown.
0000-0002-8112-0180, Abadias, Luciano, De León-Contreras, Marta, Torrea, José L.   +3 more
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Calculus of Variations with Classical and Fractional Derivatives [PDF]

, 2012
We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the
Odzijewicz, Tatiana, Torres, Delfim F. M.   +1 more
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Fractional Generalization of Gradient Systems

, 2005
We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered.
B. A. Dubrovin, C. Sparrow, E. N. Lorenz, G. M. Zaslavsky, I. Podlubny, K. B. Oldham, K. Cottrill-Shepherd, M. Caputo, M. Caputo, M. Hirsh, O. E. Rossler, R. Gilmor, R. Gorenflo, R. Nigmatullin, S. G. Samko, V. E. Tarasov, V. E. Tarasov, V. E. Tarasov, V. E. Tarasov, V. E. Tarasov, V. E. Tarasov, V. E. Tarasov, V. E. Tarasov, Vasily E. Tarasov   +23 more
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