Results 31 to 40 of about 1,913,284 (306)

FRACTIONAL DERIVATIVE AS FRACTIONAL POWER OF DERIVATIVE [PDF]

International Journal of Mathematics, 2007
Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of selfadjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator.
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Fractional Coins and Fractional Derivatives [PDF]

Abstract and Applied Analysis, 2013
This paper discusses the fundamentals of negative probabilities and fractional calculus. The historical evolution and the main mathematical concepts are discussed, and several analogies between the two apparently unrelated topics are established. Based on the new conceptual perspective, some experiments are performed shading new light into possible ...
openaire   +5 more sources

Derivation of operational matrix of Rabotnov fractional-exponential kernel and its application to fractional Lienard equation

Alexandria Engineering Journal, 2020
Our motive in this contribution is to find out the operational matrix of fractional derivative having non singular kernel namely Rabotnov fractional-exponential (RFE) kernel which is recently introduced and seeking numerical solution of non-linear ...
Sachin Kumar, J.F. Gómez-Aguilar, J.E. Lavín-Delgado, D. Baleanu   +3 more
doaj   +1 more source

On a New Modification of the Erdélyi–Kober Fractional Derivative

Fractal and Fractional, 2021
In this paper, we introduce a new Caputo-type modification of the Erdélyi–Kober fractional derivative. We pay attention to how to formulate representations of Erdélyi–Kober fractional integral and derivatives operators.
Z. Odibat, D. Baleanu
semanticscholar   +1 more source

Fractional Derivatives and the Fundamental Theorem of Fractional Calculus [PDF]

Fractional Calculus and Applied Analysis, 2020
In this paper, we address the one-parameter families of the fractional integrals and derivatives defined on a finite interval. First we remind the reader of the known fact that under some reasonable conditions, there exists precisely one unique family of the fractional integrals, namely, the well-known Riemann-Liouville fractional integrals.
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Aging and rejuvenation with fractional derivatives [PDF]

Physical Review E, 2004
We discuss a dynamic procedure that makes the fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and divergent second moment, namely with the power index mu in the interval 2>ta yields ord=mu -2.
Aquino, Gerardo, Bologna, Mauro, Grigolini, Paolo, West, Bruce J.   +3 more
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Comparative analysis for radiative slip flow of magnetized viscous fluid with mixed convection features: Atangana-Baleanu and Caputo-Fabrizio fractional simulations

Case Studies in Thermal Engineering, 2021
This novel investigation suggests interesting solution techniques regarding the magnetized flow of Casson material through a porous space confined by a vertical surface.
M. Ijaz Khan, Ali Raza, Maria Naseem, Kamel Al-Khaled, Sami Ullah Khan, M. Imran Khan, Essam Roshdy El-Zahar, M.Y. Malik   +7 more
doaj   +1 more source

Dynamical Analysis of Generalized Tumor Model with Caputo Fractional-Order Derivative

Fractal and Fractional, 2023
In this study, we perform a dynamical analysis of a generalized tumor model using the Caputo fractional-order derivative. Tumor growth models are widely used in biomedical research to understand the dynamics of tumor development and to evaluate potential
A. Padder, Laila Almutairi, S. Qureshi, Amanullah Soomro, Afroz Afroz, E. Hıncal, Asifa Tassaddiq   +6 more
semanticscholar   +1 more source

Lie symmetry analysis of (2+1)-dimensional time fractional Kadomtsev-Petviashvili equation [PDF]

Open Communications in Nonlinear Mathematical Physics
In this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional Kadomtsev-Petviashvili (KP) equation with the mixed derivative of Riemann-Liouville time-fractional derivative and integer-order $x$-derivative.
Jicheng Yu, Yuqiang Feng
doaj   +1 more source

A New Generalized Definition of Fractional Derivative with Non-Singular Kernel

De Computis, 2020
This paper proposes a new definition of fractional derivative with non-singular kernel in the sense of Caputo which generalizes various forms existing in the literature. Furthermore, the version in the sense of Riemann–Liouville is defined.
K. Hattaf
semanticscholar   +1 more source