[PDF] Top 20 A review of definitions for fractional derivatives and integral
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A review of definitions for fractional derivatives and integral
... order of the derivative emerged: What might be a derivative of order 1/2? In a prophetic answer, Leibniz foresees the beginning of the area that nowadays is named fractional calculus ...Newton ... See full document
7
RIESZ POTENTIAL OPERATORS AND INVERSES VIA FRACTIONAL CENTRED DERIVATIVES
... these definitions were proposed first by Liouville ...inside and on an infinite integration path that encircles the points t = z − kh in the forward case and t = z + kh in the corresponding backward ... See full document
12
On the relation between the fractional Brownian motion and the fractional derivatives
... definition and simulation of fractional Brownian motion are considered from the point of view of a set of coherent fractional derivative ...sets of ... See full document
12
Hyers-Ulam Stability of a Class Fractional Boundary Value Problems with Right and Left Fractional Derivatives
... A review of some background material is presented in Section ...stability of (1) is considered in Section 3. The Hyers-Ulam stability of (1) is considered in Section ...examples of ... See full document
7
Caputo derivatives of fractional variable order: numerical approximations
... presence of a standard problem, where numerous tools are available to solve ...Caputo fractional problems of variable ...needed definitions. Namely, we present three types of Caputo ... See full document
22
Fractional derivatives : generalizations = Derivadas fracionárias: generalizações
... number of different fractional integration and differentiation operators has been increasing along the last few ...Classical fractional derivatives, among which we mention the ... See full document
105
Isoperimetric problems of the calculus of variations with fractional derivatives
... bound of the integral not coinciding with the lower bound of the fractional ...result of [9] is a new Euler-Lagrange equation for the functional ...techniques of [9] to prove an ... See full document
13
Approximation of fractional integrals by means of derivatives
... left fractional integral (Eq. (12)). The order of magnitude of the coefficients that we ignore during this procedure is small for the examples that we have chosen (Tables 1 and ...aim ... See full document
15
Some properties of generalized fractional integral with Lengendre functions kernels
... derivative of order 1 2 , the fractional calculus has become a new attractive theory to the mathematicians, as well for other researcher of non-mathematician areas (biology, economy, physics, ... See full document
8
Regional enlarged observability of fractional differential equations with Riemann—Liouville time derivatives
... studies of Euler (1730), Lagrange (1772), Laplace (1812), Fourier (1822), Abel (1823), Liouville (1832), Riemann (1847), Greer (1859), Grünwald (1867), Laurent (1884), Heaviside (1892), Pincherle (1902), Marchaud ... See full document
13
An expansion formula with higher-order derivatives for fractional operators of variable order
... outline of the paper is the ...necessary definitions, namely, the fractional operators of Riemann-Liouville and Marchaud of variable ...properties of the operators are ... See full document
12
Further properties of Osler's generalized fractional integrals and derivatives with respect to another function
... derivative and integral with respect to another function ...choices of ψ, we obtain some well known definitions, like the Riemann–Liouville [10, 15, 18, 20, 35], the Hadamard [4, 5, 13] ... See full document
35
Fractional Euler-Lagrange differential equations via Caputo derivatives
... We review some recent results of the fractional variational ...conditions of Euler–Lagrange type for functionals with a La- grangian containing left and right Caputo derivatives ... See full document
10
Fractional differential equations and Volterra–Stieltjes integral equations of the second kind
... we review some necessary concepts and results on fractional ...ψ-Caputo fractional derivative of order α > 1 and prove several results concerning this problem which will be ... See full document
21
Boundary value problems for nonlinear fractional differential equations and inclusions with nonlocal and fractional integral boundary conditions
... Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and ...characteristics of the ... See full document
22
Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative
... we review some concepts of fractional ...left and right Hadamard fractional integrals are given in Section 3, together with approximation formulas and error ...left and ... See full document
16
Duality for the left and right fractional derivatives
... the definitions of fractional calculus needed in the ...left and right fractional ...left and right fractional derivatives or integrals is independent of the ... See full document
15
Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems
... old and yet an interesting topic [1]. It deals with the investigation of integrals and derivatives of an arbitrary ...the fractional derivative was a mathematical tool without a ... See full document
30
Caputo–Hadamard fractional derivatives of variable order
... integer-order derivatives in the seventeenth century, L’Hˆ opital and Leibniz wondered about the notion of derivative of order n = ...works of Fourier, Riemann, Liouville, Hadamard, Gr¨ ... See full document
14
Fractional Central Differences and Derivatives
... For those differences, we presented integral representations, from which we obtained the derivative integrals, similar to Cauchy derivatives, using the properties of the Gamma function..[r] ... See full document
12
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