A Single and Multi‐Valued Problems Involving Mixed (k1,η)‐Hilfer and (k2,ϕ)‐Hilfer Fractional Derivatives for the Fractional Navier Problem
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DOI: 10.1002/mma.10993
Abstract: This paper investigates fractional differential equations and inclusions involving two distinct fractional derivatives, specifically the (k1,η)$$ \left({k}_1,\eta \right) $$ ‐Hilfer and (k2,ϕ)$$ \left({k}_2,\phi \right) $$ ‐Hilfer fractional derivatives, within the framework of the Navier boundary… read more here.
Keywords: hilfer fractional; problem single; fractional derivatives; hilfer ... See more keywords
On the variable-order fractional derivatives with respect to another function
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DOI: 10.1007/s00010-024-01082-0
Abstract: In this paper, we present various concepts concerning generalized fractional calculus, wherein the fractional order of operators is not constant, and the integral kernel depends on a function. We observe that in the case of… read more here.
Keywords: variable order; order fractional; function; fractional derivatives ... See more keywords
Variational problems of Herglotz type with complex order fractional derivatives and less regular Lagrangian
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DOI: 10.1007/s00707-019-02521-9
Abstract: We derive optimality conditions for variational problems of Herglotz type whose Lagrangian depends on fractional derivatives of both real and complex order, and resolve the case of subdomain when the lower bounds of variational integral… read more here.
Keywords: complex order; herglotz type; fractional derivatives; problems herglotz ... See more keywords
Functionality of circuit via modern fractional differentiations
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DOI: 10.1007/s10470-018-1371-6
Abstract: The significance of the modern fractional derivatives containing the singular kernel with locality and the non-singular kernel with non-locality have recently diverted the researchers because of the numerical or experimental analyses on the behavior between… read more here.
Keywords: circuit via; modern fractional; circuit; rlc electrical ... See more keywords
Applications of fractional derivatives for Alexander integral operator
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DOI: 10.1007/s13370-020-00852-8
Abstract: Let $$T_n$$ T n be the class of functions $$f(z)=z+a_{n+1}z^{n+1}+a_{n+2}z^{n+2}+\ldots $$ f ( z ) = z + a n + 1 z n + 1 + a n + 2 z n + 2… read more here.
Keywords: lambda; alexander integral; derivatives alexander; fractional derivatives ... See more keywords
Hilfer–Katugampola fractional derivatives
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DOI: 10.1007/s40314-017-0536-8
Abstract: We propose a new fractional derivative, the Hilfer–Katugampola fractional derivative. Motivated by the Hilfer derivative this formulation interpolates the well-known fractional derivatives of Hilfer, Hilfer–Hadamard, Riemann–Liouville, Hadamard, Caputo, Caputo–Hadamard, Liouville, Weyl, generalized and Caputo-type. As… read more here.
Keywords: derivatives hilfer; caputo; hilfer katugampola; katugampola fractional ... See more keywords
Fractional transform methods for coupled system of time fractional derivatives of non-homogeneous Burgers’ equations arise in diffusive effects
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DOI: 10.1007/s40314-019-0829-1
Abstract: The coupled system of time fractional derivatives of non-homogeneous Burgers’ equations is solved both analytically and numerically. The approximate analytical solutions of power series type are obtained by the fractional homotopy analysis transform method, which… read more here.
Keywords: fractional derivatives; derivatives non; transform; system time ... See more keywords
Solutions of 1-D Dispersive Equation with Time and Space-Fractional Derivatives
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DOI: 10.1007/s40819-017-0462-x
Abstract: This paper applied Adomian decomposition method to obtain the solution of fractional third-order dispersive equation with time and space-fractional derivatives. The iterative technique is carried out in a straightforward manner without the need for transforms… read more here.
Keywords: equation time; space fractional; dispersive equation; time space ... See more keywords
Some Inequalities Involving Fractional q-Derivatives Related to the q-Leibniz Rule
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DOI: 10.1007/s40840-018-0655-4
Abstract: In this paper, we present some inequalities for Riemann–Liouville and Caputo q-fractional derivatives related to the q-Leibniz rule. We used one of the inequalities to prove the maximum principle for a time fractional q-Cauchy differential… read more here.
Keywords: leibniz rule; derivatives related; inequalities involving; fractional derivatives ... See more keywords
Approximate limit cycles of coupled nonlinear oscillators with fractional derivatives
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DOI: 10.1016/j.apm.2019.08.028
Abstract: Abstract In this paper, the homotopy analysis method (HAM) is presented to establish the accurate approximate analytical solutions for multi-degree-of-freedom (MDOF) coupled nonlinear oscillators with fractional derivatives. Approximate limit cycles (LCs) of two systems of… read more here.
Keywords: limit cycles; nonlinear oscillators; approximate limit; oscillators fractional ... See more keywords
On-line estimation of the Caputo fractional derivatives with application to PIµDν control
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DOI: 10.1016/j.ifacol.2020.12.2552
Abstract: This paper proposes new procedures for calculation of the Caputo derivative of model-free measured signals. The evaluation of the non-integer derivative is realized by integrating a set of ordinary differential equations and convolution. The derivative… read more here.
Keywords: estimation caputo; fractional derivatives; derivatives application; line estimation ... See more keywords