[PDF] Top 20 Caputo–Hadamard fractional derivatives of variable order
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Caputo–Hadamard fractional derivatives of variable order
... types of Caputo–Hadamard derivatives of variable fractional order, and study the relations between ...each fractional operator, using integer-order ... See full document
14
Variational Problems Involving a Caputo-Type Fractional Derivative
... calculus of variations problems, where the Lagrange function depends on the Caputo-Katugampola fractional ...type of fractional operator is a generalization of the Caputo ... See full document
15
Application of Bernoulli polynomials for solving variable-order fractional optimal control-affine problems
... solving variable-order fractional optimal control-affine ...The variable-order fractional derivative is considered in the Caputo sense, which together with the ... See full document
18
Calculus of variations involving Caputo-Fabrizio fractional differentiation
... meaning of derivatives with integer order be generalized to derivatives with non-integer orders?” L’Hospital was curious about that question and replied by another question to Leibniz: “What ... See full document
10
Fractional derivatives: The perspective of system theory
... name fractional derivative (FD) is assigned to several mathematical operators, namely the Grünwald-Letnikov (GL), Liouville (L), Riemann-Liouville (RL), Caputo (C), Marchaud, Hadamard (H), Riesz, and ... See full document
14
Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators using Caputo derivatives
... The fractional Laplace appears ...generators of the stable L´ evy processes ...the fractional Laplace in mechanics and in elastostatics [3] or fluid dynamics ...a fractional Laplace operator ... See full document
13
Enlarged controllability and optimal control of sub-diffusion processes with Caputo fractional derivatives
... help of optimization theory. Optimal control, as a branch of Mathematics, aims to improve the state variables of a control system in order to maximize the benefit or minimize the given ... See full document
13
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 to another ...the fractional derivative of a power ... See full document
27
Functional differential equations involving the ψ-Caputo fractional derivative
... ψ-Caputo fractional derivative. By choosing this type of derivative, we present some results valid for a wide class of ...collection of works dealing with these issues for different ... See full document
8
Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators
... a fractional Laplace operator in 3-dimensional space using Caputo derivatives with different order of differentiation for each ...type of operators where considered in [15], [3], ... See full document
8
Isoperimetric problems of the calculus of variations with fractional derivatives
... basic fractional isoperimetric problem and prove correspondent necessary optimality conditions, both for normal and abnormal extremizers (Theorems 6 and 7, ...bound of the integral is greater than the lower ... See full document
13
Duality for the left and right fractional derivatives
... correspondence of 1695, L’Hopital proposed the following problem to Leibniz: “Can the meaning of derivatives with integer order be generalized to noninteger orders?” Since then, several ... See full document
15
The stability and stabilization of infinite dimensional Caputo-time fractional differential linear systems
... Fractional order calculus is a natural generalization of classical integer order ...and derivatives of an arbitrary real or complex ...order. Fractional ... See full document
14
Caputo fractional differential equation with state dependent delay and practical stability
... properties of Caputo fractional delay differential equations is studied and, in particular, the case with state dependent delays is con- ...type of delays is a generalization of several ... See full document
28
A coherent approach to non-integer order derivatives
... the fractional differences to the fractional derivative defined in the complex plane, obtaining the well-known Cauchy ...analysis of the generalised Cauchy integral is done in Section 3 with the help ... See full document
11
Caputo derivatives of fractional variable order: numerical approximations
... presence of a standard problem, where numerous tools are available to solve ...to Caputo fractional problems of variable ...types of Caputo derivatives of ... See full document
22
Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative
... We obtained approximation formulas for the Hadamard fractional integrals and derivatives, and an upper bound for the error on such decompositions. In this section we will study several cases, ... See full document
16
An expansion formula with higher-order derivatives for fractional operators of variable order
... extension of the integer- order calculus by considering derivatives and integrals of arbitrary real or complex order 𝛼 ∈ K, with K = R or K = ...Recently, fractional calculus has ... See full document
12
Fractional Euler-Lagrange differential equations via Caputo derivatives
... meaning of derivative be generalized to derivatives of non-integer order?” Since then, several mathematicians had investigated Leib- niz’s challenge, among them Liouville, Riemann, Weyl, and ... See full document
10
Constrained fractional variational problems of variable order
... combined Caputo derivative of variable fractional order, and present some properties that will be need in the ...in order to determine the minimizers for each of the ... See full document
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