Variable-order fractional calculus
An expansion formula with higher-order derivatives for fractional operators of variable order
... the order 𝛼 of the integrals and derivatives may take any value, another interesting extension is to consider the order not as a constant during the process but as a variable 𝛼(𝑡) that depends on ...
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Application of Bernoulli polynomials for solving variable-order fractional optimal control-affine problems
... The variable-order fractional calculus was introduced in 1993 by Samko and Ross and deals with operators of order α, where α is not necessarily a constant but a function α ( t ) of time ...
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Calculus of variations on time scales and discrete fractional calculus
... discrete fractional calculus theory we proved some properties for the fractional sum and difference operators in Section ...discrete fractional calculus is the existence of solutions to ...
116
Fractional calculus of variations
... the fractional calculus of variations with a Lagrangian depending on fractional derivatives has emerged as an elegant alternative to study non-conservative ...presented fractional variational ...
156
Computational methods in the fractional calculus of variations and optimal control
... on fractional optimal control problems by considering the end time, T , free and the dynamic control system ...and fractional order ...a variable number with a < T < ...state ...
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Constrained fractional variational problems of variable order
... of variable fractional ...for fractional variational problems with Lagrangians containing left-sided and right-sided fractional derivatives of variable ...“multi-term fractional ...
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Caputo derivatives of fractional variable order: numerical approximations
... of fractional calculus consists to allow the fractional order of the derivative to be non-constant, depending on time [5, 19, ...such fractional operators, is the extreme difficulty in ...
22
Caputo–Hadamard fractional derivatives of variable order
... ordinary calculus was developed for integer-order derivatives in the seventeenth century, L’Hˆ opital and Leibniz wondered about the notion of derivative of order n = ...of fractional ...
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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 order of the derivative is taken as a free ...
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A fractional calculus of variations for multiple integrals with application to vibrating string
... Jumarie fractional integral and derivative, 29 , 28 , 30 extending such notions to the multidimensional ...Jumarie fractional derivative is equal to the standard one and, as we show, the fractional ...
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Chain rules and inequalities for the BHT fractional calculus on arbitrary timescales
... differential calculus, does not hold for the BHT fractional ...and fractional differentiable of order α ∈ (0, 1] at t ∈ T κ and f : R → R is continuously differentiable, then there exists c ∈ ...
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A fractional calculus of variations for multiple integrals with application to vibrating string
... non-integer order derivatives and integrals in different areas of physics and mathematics [12, 23, ...variational calculus, and optimal control [19, 22, ...
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Embeddings of variable Hajlasz-Sobolev spaces into holder spaces of variable order
... The case when the exponent is greater than the dimension of the Euclidean space R n was less studied. The first attempt to get Sobolev embeddings into Hölder classes of variable order was done in [10]. Later ...
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A Low-Dropout Voltage Regulator with a Fractional-Order Control
... A low-dropout voltage regulator using a fractional- order control was presented. Accurate voltage regulation with a low dynamic output resistance of approximately 300 m Ω was achieved while maintaining a ...
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A time-fractional Borel-Pompeiu formula and a related hypercomplex operator calculus
... During the last decades, Clifford analysis proved to be a good tool to study partial differential equations of mathematical-physics. In particular, we have the work of G¨ urlebeck and Spr¨ oßig based on a Borel-Pompeiu ...
22
Stability analysis of a fractional-order HBV infection model
... Fractional calculus is an area of mathematics that addresses generalization of the mathematical operations of differ- entiation and integration to arbitrary (non-integer) ...years, fractional ...
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Fractional order optimal control problems with free terminal time
... dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminal- time triplet to be optimal are obtained. Situations ...
19
A Subclass of Uniformly Convex Functions Associated with Certain Fractional Calculus Operator
... a certain fractional calculus operator. The class has interesting subclasses like β-uniformly starlike, β- uniformly convex and β-uniformly pre-starlike func- tions. Properties like coefficient estimates, ...
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Control of a novel chaotic fractional order system using a state feedback technique
... where fractional calculus has initi- ated its success and activity in engineering applications, is referred to [20,21] ...a fractional order chaotic system. The corresponding ...
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Optimal Control and Sensitivity Analysis of a Fractional Order TB Model
... This function measures the proportional variation in the number of infectious individuals after the application of the control u ∗ , by comparing the number of infected individuals at ti[r] ...
9