Results 41 to 50 of about 14,096 (164)

A new fractional derivative extending classical concepts: Theory and applications

Partial Differential Equations in Applied Mathematics
In this paper, a novel general definition for the fractional derivative and fractional integral based on an undefined kernel function is introduced.
Mutaz Mohammad, Mohamed Saadaoui
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Exact results for a fractional derivative of elementary functions

SciPost Physics, 2018
We present exact analytical results for the Caputo fractional derivative of a wide class of elementary functions, including trigonometric and inverse trigonometric, hyperbolic and inverse hyperbolic, Gaussian, quartic Gaussian, and Lorentzian ...
Gavriil Shchedrin, Nathanael C. Smith, Anastasia Gladkina, Lincoln D. Carr
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Time-Fractional Differential Equations with an Approximate Solution

Journal of Nigerian Society of Physical Sciences, 2022
This paper shows how to use the fractional Sumudu homotopy perturbation technique (SHP) with the Caputo fractional operator (CF) to solve time fractional linear and nonlinear partial differential equations.
Lamees K. Alzaki, Hassan Kamil Jassim
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Hydromagnetic free convection flow of viscous fluid between vertical parallel plates with damped thermal and mass fluxes

Alexandria Engineering Journal, 2019
In this article, hydromagnetic free convection flow of viscous fluid between two vertical plates is considered. The Caputo time-fractional derivative is used and the governing equations are fractionalized by means of generalized Fourier’s and Fick’s laws.
Zehui Shao, Nehad Ali Shah, Iskander Tlili, Usman Afzal, M. Saqib Khan   +4 more
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A remark on local fractional calculus and ordinary derivatives

Open Mathematics, 2016
In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary
Almeida Ricardo, Guzowska Małgorzata, Odzijewicz Tatiana   +2 more
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General Fractional Calculus: Multi-Kernel Approach

Mathematics, 2021
For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In Luchko works, the proposed approaches to formulate this calculus are based either on the power of one Sonin kernel or the convolution of one ...
Vasily E. Tarasov
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Generalized time fractional IHCP with Caputo fractional derivatives

Journal of Physics: Conference Series, 2008
The numerical solution of the generalized time fractional inverse heat conduction problem (GTFIHCP) on a finite slab is investigated in the presence of measured (noisy) data when the time fractional derivative is interpreted in the sense of Caputo. The GTFIHCP involves the simultaneous identification of the heat flux and temperature transient functions
D A Murio, C E Mejía
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Fractional calculus of variations with a generalized fractional derivative [PDF]

Fractional Differential Calculus, 2016
Summary: In this paper, we introduce a generalization of the Hilfer-Prabhakar derivative and obtain the Euler-Lagrange equations and Hamiltonian formulation with respect to this fractional derivative in the theory of fractional calculus of variations. Also, we get a sufficient condition for optimality.
Askari, Hassan, Ansari, Alireza
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Generalized fractional derivatives and Laplace transform

Discrete & Continuous Dynamical Systems - S, 2020
The authors consider a general form of fractional derivative; namely $g$-fractional derivatives, where the kernel $g$ is a function on the space of absolutely continuous functions. They generalized the Laplace transform in order to be applicable for $g$-fractional derivatives and apply this transform to solve some fractional differential equations.
Jarad, Fahd, Abdeljawad, Thabet
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A new Generalized fractional derivative and integral

, 2017
In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional derivative such as Product Rule, Quotient Rule, Chain Rule, Roll's Theorem and Mean Value Theorem.
AKKURT, Abdullah, YILDIRIM, Merve Esra, YILDIRIM, Hüseyin   +2 more
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