Riemann-Liouville fractional order
Monotone method for Riemann-Liouville multi-order fractional differential systems
... nonlinear fractional differential equations, much as in the integer order case, this does not necessarily imply that calculating a solution explicitly will be routine, or even ...on fractional ...
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Fractional order optimal control problems with free terminal time
... and Riemann–Liouville fractional operators, and then use ( 1 ) and ( 2 ...of fractional order optimal ...Caputo fractional derivatives, which is stated in the following ...
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Caputo–Hadamard fractional derivatives of variable order
... the order of the derivative a real valued function α : [a, b] → (0, ...the Riemann–Liouville fractional ...these fractional operators are nonlocal, and contain memory about the past ...
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Application of Bernoulli polynomials for solving variable-order fractional optimal control-affine problems
... the fractional calculus of variations [ 10 – 12 ]. Soon after, fractional optimal control theory became a mature research area, supported with many applications in engineering and ...of fractional ...
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Fundamental solution for natural powers of the fractional Laplace and Dirac operators in the Riemann-Liouville sense
... about fractional calculus and Cliord ...n-parameter fractional Laplace operator, being this the key for the paper, because it connects the fundamental solution of previous order of the powers of the ...
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An expansion formula with higher-order derivatives for fractional operators of variable order
... the fractional operators of Riemann-Liouville and Marchaud of variable ...considered fractional operators, with the size of the expansion being the derivative of order 𝑛 ∈ ...variable ...
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Eigenfunctions and Fundamental Solutions of the Fractional Laplace and Dirac Operators: The Riemann-Liouville Case
... Clifford analysis is a generalization of classical complex analysis in the plane to the case of an arbitrary dimension. At the heart of the theory lies the Dirac operator D, a conformally invariant first-order ...
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A numerical method to solve higher-order fractional differential equations
... integer order was pertinent and Leibniz himself wondered about the derivative of order α = ...1/2. Liouville carried out a serious investigation on the subject, and presented a notion of ...
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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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General fractional-order anomalous diffusion with non-singular power-law kernel
... the Riemann-Liouville and Liou- ville-Caputo GFD with non-singular power-law ...and Liouville-Caputo general fractional time anomalous diffusion models with non-singular power-law kernel were ...
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Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative
... involving fractional operators, such as fractional differential equations, control problems, etc, is that solving them analytically has proven to be hard or even ...Hadamard fractional operators with ...
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Regional enlarged observability of fractional differential equations with Riemann—Liouville time derivatives
... (1823), Liouville (1832), Riemann (1847), Greer (1859), Grünwald (1867), Laurent (1884), Heaviside (1892), Pincherle (1902), Marchaud (1927), Love (1938), Widder (1941), Riesz (1949), Feller (1952), among ...
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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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Fuzzy, integer and fractional order control: application on a wind turbine benchmark model
... Currently, the wind energy conversion system (WECS) deployment is in expansion, contributing to an increase share of converting renewable energy into electric energy. In 2012, wind power exploitation has a growth of 19.2 ...
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An optimization method for the best fractional order to estimate real data analysis
... considering fractional derivatives, we have an infinite choices of derivative orders that we can choose, and with it determine what is the best fractional differential equation that fits better in the ...
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A Integral de Riemann-Stieltjes / The Riemann-Stieltjes Integral
... de Riemann: a integral de ...de Riemann-Stieltjes preserva muitas propriedades da integral de Riemann, algumas delas, apresentadas neste ...de Riemann-Stieltjes pode ser convertida em uma soma ...
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A MULTIGRID ACCELERATED HIGH-ORDER COMPACT FRACTIONAL-STEP METHOD FOR UNSTEADY INCOMPRESSIBLE VISCOUS FLOWS
... in order to avoid spurious oscillations in the pressure ...second order Adams-Bashford method without considering the pressure terms in the predictor step, the velocity field is then corrected such that ...
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Teorema de Riemann-Roch, morfismos de Frobenius e a hipótese de Riemann
... de Riemann, em especial ao teorema de ...de Riemann vale para o caso de curvas sobre corpos finitos, sem contar que ele ´e usado fortemente na prova da racionalidade da ...de Riemann-Roch ´e uma ...
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Surfaces with Prescribed Nodes and Minimum Energy Integral of Fractional Order
... Alghofari studied the problem of finding a sufficiently smooth function on a square domain that minimizes an energy integral and assumes specified values on a re[r] ...
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Control of a novel chaotic fractional order system using a state feedback technique
... [33] , and active control [34] . The main problem in applying such control methodologies for taming chaos is often their complexity in implementation. In this paper we propose a simple linear con- trol mechanism, based ...
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