Fractional Riemann–Liouville derivatives
Fischer Decomposition and Cauchy-Kovalevskaya extension in fractional Clifford analysis: the Riemann-Liouville case
... a fractional function theory in higher dimensions by means of a fractional correspondence to the Weyl relations via fractional Riemann-Liouville ...decomposition, fractional ...
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Regional enlarged observability of fractional differential equations with Riemann—Liouville time derivatives
... Abstract: We introduce the concept of regional enlarged observability for fractional evolution differential equations involving Riemann–Liouville derivatives. The Hilbert Uniqueness ...
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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, ...the Riemann-Liouville ...
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Caputo–Hadamard fractional derivatives of variable order
... with fractional operators, we find different numerical approaches to solve the desired ...integer-order derivatives only [1, 12, ...involving fractional operators, we can simply replace them with the ...
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Duality for the left and right fractional derivatives
... of derivatives with integer order be generalized to noninteger orders?” Since then, several mathematicians studied this question, among them Liouville, Riemann, Weyl and ...the fractional ...
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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), ...
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Variational methods for the solution of fractional discrete/continuous Sturm-Liouville problems
... the Riemann–Liouville is ...solving fractional differential equations, of the Riemann-Liouville derivative contains the limit values of the Riemann-Liouville ...
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Approximation of fractional integrals by means of derivatives
... a fractional integral equation (Example 6.1) and a fractional variational problem in which the Lagrangian depends on the left Riemann–Liouville frac- tional integral (Example ...the ...
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Fractional Euler-Lagrange differential equations via Caputo derivatives
... to derivatives of non-integer order?” Since then, several mathematicians had investigated Leib- niz’s challenge, among them Liouville, Riemann, Weyl, and ...of fractional calculus, ...
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RIESZ POTENTIAL OPERATORS AND INVERSES VIA FRACTIONAL CENTRED DERIVATIVES
... results: Riemann-Liouville, Caputo, Gr¨unwald-Letnikov, Hadamard, Marchaud, are some of the known definitions ...a fractional systems theory coherent with the usual practice and accepted notions and ...
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Fundamental solution for natural powers of the fractional Laplace and Dirac operators in the Riemann-Liouville sense
... three-parameter fractional Laplace operator de ned with Caputo and Riemann-Liouville fractional derivatives, and derived also fundamental solutions for the corresponding ...
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An expansion formula with higher-order derivatives for fractional operators of variable order
... considering derivatives and integrals of arbitrary real or complex order 𝛼 ∈ K, with K = R or K = ...Abel, Liouville, and Riemann, just to mention a few ...Recently, fractional calculus has ...
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Enlarged controllability and optimal control of sub-diffusion processes with Caputo fractional derivatives
... of fractional order began more than three centuries ...Fourier, Liouville, Grunwald, Letnikov and ...new fractional derivatives [ 1 , 2 , 3 , 4 , 5 ...decades, fractional calculus has ...
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Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative
... terms, Fractional Calculus allows us to define integrals and derivatives of arbitrary real order, and can be seen as a generalization of ordinary ...A fractional derivative of order α > 0, when α ...
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Further properties of Osler's generalized fractional integrals and derivatives with respect to another function
... the Riemann–Liouville [10, 15, 18, 20, 35], the Hadamard [4, 5, 13] and the Erd´ elyi–Kober fractional operators [14, ...of fractional derivative was studied, and a Leibniz and chain formulas ...
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Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators using Caputo derivatives
... The fractional Laplace appears ...the fractional Laplace in mechanics and in elastostatics [3] or fluid dynamics ...a fractional Laplace operator in 3-dimensional space using Caputo ...
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Eigenfunctions and Fundamental Solutions of the Fractional Laplace and Dirac Operators: The Riemann-Liouville Case
... in fractional calculus increased ...of fractional derivatives like, for example, in optics and quantum mechanics, and on the other hand fractional calculus gives us a new degree of freedom ...
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Existence and uniqueness of solution for a fractional Riemann-Liouville initial value problem on time scales
... Along the work, we consider the order a of the fractional derivatives in the real interval ð0; 1Þ. We can, however, easily generalize our definition of fractional derivative to any positive real a. ...
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A Integral de Riemann-Stieltjes
... de Riemann-Stieltjes surgiu com o intuito de suprir carências da integral de Riemann em relação, principalmente, à ...de Riemann, mas há resultados na Teoria de Probabilidade ou na Análise Funcional, ...
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Gleason’s problem associated to the fractional cauchy-riemann operator, fueter series, drury-arveson space and related topics
... Abstract. In this paper we present the building blocks for a function theory based on fractional Cauchy-Riemann operators. We are going to construct basic monogenic powers and Fueter series. With these ...
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