Results 21 to 30 of about 41,470 (233)

Fractional Cauchy Problem with Caputo Nabla Derivative on Time Scales

Abstract and Applied Analysis, 2015
The definition of Caputo fractional derivative is given and some of its properties are discussed in detail. After then, the existence of the solution and the dependency of the solution upon the initial value for Cauchy type problem with fractional Caputo
Jiang Zhu, Ling Wu
doaj   +1 more source

Heat transfer analysis in a non-Newtonian hybrid nanofluid over an exponentially oscillating plate using fractional Caputo–Fabrizio derivative

Scientific Reports, 2022
In this paper, we have been study a hybrid nanofluid over an exponentially oscillating vertical flat plate. Therefore the fractional derivatives definition of Caputo–Fabrizio approach is applied to transform the classical model for this hybrid nanofluid ...
Sami Ul Haq, Naveed Mahmood, Saeed Ullah Jan, Sehra, Ilyas Khan, Abdullah Mohamed   +5 more
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Fractional Probability Theory of Arbitrary Order

Fractal and Fractional, 2023
A generalization of probability theory is proposed by using the Riemann–Liouville fractional integrals and the Caputo and Riemann–Liouville fractional derivatives of arbitrary (non-integer and integer) orders. The definition of the fractional probability
Vasily E. Tarasov
doaj   +1 more source

Modeling and analysis of competition model of bank data with fractal-fractional Caputo-Fabrizio operator

Alexandria Engineering Journal, 2020
The present paper consider a newly introduced operator known as fractal-fractional where the fractional operator considered is Caputo-Fabrizio. We consider a competition system and propose the field data of banks for 2004–2014 of Indonesia banks of the ...
Abdon Atangana, Muhammad Altaf Khan, Fatmawati   +2 more
doaj   +1 more source

Fractal–fractional and stochastic analysis of norovirus transmission epidemic model with vaccination effects

Scientific Reports, 2021
In this paper, we investigate an norovirus (NoV) epidemic model with stochastic perturbation and the new definition of a nonlocal fractal–fractional derivative in the Atangana–Baleanu–Caputo (ABC) sense.
Ting Cui, Peijiang Liu, Anwarud Din
doaj   +1 more source

Infrared spectroscopy of diatomic molecules - a fractional calculus approach

, 2012
The eigenvalue spectrum of the fractional quantum harmonic oscillator is calculated numerically solving the fractional Schr\"odinger equation based on the Riemann and Caputo definition of a fractional derivative.
Dirac P. A. M., Eid R., Erdelyi A., Greiner W., Herrmann R., Herrmann R., Herzberg G., Huygens C., Khunrath H., Krause K., Lissajous J. A., Lusztig R., Messiah A., Oldham K. B., Parisi G., Podlubny I., RICHARD HERRMANN, Rubin B., Seybold H. J., Villeneuve D. M., Whitten K. W.   +20 more
core   +1 more source

Applications of Lyapunov Functions to Caputo Fractional Differential Equations

Mathematics, 2018
One approach to study various stability properties of solutions of nonlinear Caputo fractional differential equations is based on using Lyapunov like functions.
Ravi Agarwal, Snezhana Hristova, Donal O’Regan   +2 more
doaj   +1 more source

A hybrid B-spline collocation technique for the Caputo time fractional nonlinear Burgers’ equation

Beni-Suef University Journal of Basic and Applied Sciences, 2023
Background This study proposes an efficient and stable technique based on new hybrid B-spline (HB-spline) functions for the numerical treatment of the Caputo time fractional nonlinear Burgers’ (TFNB) equation. The time derivative is discretized using the
Mohammad Tamsir, Deependra Nigam, Neeraj Dhiman, Anand Chauhan   +3 more
doaj   +1 more source

Covariant fractional extension of the modified Laplace-operator used in 3D-shape recovery

, 2011
Extending the Liouville-Caputo definition of a fractional derivative to a nonlocal covariant generalization of arbitrary bound operators acting on multidimensional Riemannian spaces an appropriate approach for the 3D shape recovery of aperture afflicted ...
Herrmann, Richard
core   +1 more source

Solutions of a three-dimensional multi-term fractional anomalous solute transport model for contamination in groundwater.

PLoS ONE, 2023
The study presents a meshless computational approach for simulating the three-dimensional multi-term time-fractional mobile-immobile diffusion equation in the Caputo sense. The methodology combines a stable Crank-Nicolson time-integration scheme with the
Imtiaz Ahmad, Ihteram Ali, Rashid Jan, Sahar Ahmed Idris, Mohamed Mousa   +4 more
doaj   +1 more source