[PDF] Top 20 A Caputo fractional derivative of a function with respect to another function
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A Caputo fractional derivative of a function with respect to another function
... the Caputo fractional derivative of a function with respect to another ...Riemann–Liouville fractional derivative with respect ... See full document
27
A Discretization of the Hadamard fractional derivative
... the fractional operator is replaced by a finite sum involving only integer-order derivatives of the ...the fractional derivative by this sum, we rewrite the initial problem in terms of ... See full document
9
Calculus of variations involving Caputo-Fabrizio fractional differentiation
... Although fractional calculus have various fields of applications, in this paper we are interested in the fractional calculus of variations which deals with optimization of ... See full document
10
Caputo–Hadamard fractional derivatives of variable order
... order of the derivative a real valued function α : [a, b] → (0, ...direction of research, and was studied for the first time in [16] with respect to the Riemann–Liouville ... See full document
14
B-spline and neuro-fuzzy models design with function and derivative equalities
... the derivative of a multidimensional sub-model is another multidimensional sub-model, with the same number of uni-dimensional sub-models, all with the same order, except the one ... See full document
7
Caputo derivatives of fractional variable order: numerical approximations
... generalization of the theory of fractional calculus consists to allow the fractional order of the derivative to be non-constant, depending on time [5, 19, ...20]. ... See full document
22
Enlarged controllability and optimal control of sub-diffusion processes with Caputo fractional derivatives
... Calculus of fractional order began more than three centuries ...reply to l’Hˆopital, addressing the question whether the derivative remains valid for a non-integer ...kind of operators ... See full document
13
What is the best fractional derivative to fit data?
... extension of ODE’s, where the order of the derivative may take any real positive value [6, ...what fractional derivative is to be considered, since there are various definitions ... See full document
11
On a linear-quadratic problem with Caputo derivative
... problem with a fractional control system containing a Caputo derivative of unknown ...gradient of the cost functional under given ...projection of the gradient methods for ... See full document
20
Caputo fractional differential equation with state dependent delay and practical stability
... cause of their applications in various fields of engineering and science (see, for example, the monographs [4, 13], and the cited therein ...types of delays arise in differential equations due ... See full document
28
Fractional Euler-Lagrange differential equations via Caputo derivatives
... need to complement the Euler–Lagrange equation with an appropriate natural boundary ...reader to [23, 24] and references therein. Another important family of variational problems is the ... See full document
10
Ulam stability for fractional differential equations in the sense of Caputo operator
... advantage of Caputo fractional derivative is that the fractional differential equations with Caputo frac- tional derivative use the initial conditions (including ... See full document
5
Options listing and the volatility of the underlying asset: a study on the derivative market function
... lot of misunderstanding about derivative ...kind of casinos and have no utility to the ...effects of options introduction in the Brazilian market, seeking for another benefit for ... See full document
11
Cartan geometry of spacetimes with a nonconstant cosmological function Lambda
... cosmological function could be used to model dark energy that changes along space and time, in which way it might give an alternative description for one of the models for time-evolving dark energy ... See full document
6
Approximate analytical solution of diffusion equation with fractional time derivative using optimal homotopy analysis method
... used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial ...The fractional derivatives are considered in the Caputo ... See full document
15
Further properties of Osler's generalized fractional integrals and derivatives with respect to another function
... Introduction. Fractional calculus is an important research field, not only in pure mathematics, but in applied mathematics, physics, biology, engineering, economics, ...integrals of arbitrary real or ... See full document
35
Functional differential equations involving the ψ-Caputo fractional derivative
... realistic to model real phenomena, since they take into consideration delays in the problem formulation ...generalization of the concept of differential equations with delayed arguments, where ... See full document
8
Variational Problems Involving a Caputo-Type Fractional Derivative
... the Caputo fractional derivative coincides with the Riemann–Liouville fractional ...The Caputo–Hadamard derivative is a very recent concept [11, 12], and it combines the ... See full document
15
Fractional variational problems with the Riesz-Caputo derivative
... for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo ...interval of integration of the functional is different from the interval of the ... See full document
7
A numerical study of fractional relaxation–oscillation equations involving ψ-Caputo fractional derivative
... behavior of a viscoelastic material using a spring and a dashpot in ...process with a controlled phase ...y of a system responding to an external forcing f ... See full document
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