Results 11 to 20 of about 15,213 (267)
Fuzzy Generalized Conformable Fractional Derivative [PDF]
Advances in Fuzzy Systems, 2020 We give a new definition of fuzzy fractional derivative called fuzzy conformable fractional derivative. Using this definition, we prove some results and we introduce new definition of generalized fuzzy conformable fractional derivative.
Atimad Harir +2 more
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Green’s theorem for generalized fractional derivatives [PDF]
Fractional Calculus and Applied Analysis, 2013 We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case when the generalized operators are reduced to the standard partial fractional derivatives and fractional integrals in
Odzijewicz, T. +2 more
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A Generalized Definition of the Fractional Derivative with Applications
Mathematical Problems in Engineering, 2021 A generalized fractional derivative (GFD) definition is proposed in this work. For a differentiable function expanded by a Taylor series, we show that D α
M. Abu-Shady, Mohammed K. A. Kaabar
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Generalized Hamilton's principle with fractional derivatives [PDF]
Journal of Physics A: Mathematical and Theoretical, 2010 We generalize Hamilton's principle with fractional derivatives in Lagrangian $L(t,y(t),{}_0D_t^\al y(t),α)$ so that the function $y$ and the order of fractional derivative $α$ are varied in the minimization procedure. We derive stationarity conditions and discuss them through several examples.
Atanacković, Teodor +3 more
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Fractional calculus of variations with a generalized fractional derivative [PDF]
Fractional Differential Calculus, 2016 Summary: In this paper, we introduce a generalization of the Hilfer-Prabhakar derivative and obtain the Euler-Lagrange equations and Hamiltonian formulation with respect to this fractional derivative in the theory of fractional calculus of variations. Also, we get a sufficient condition for optimality.
Askari, Hassan, Ansari, Alireza
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General Fractional Integrals and Derivatives of Arbitrary Order [PDF]
Symmetry, 2021 In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases. First, a suitable generalization of the Sonine condition is presented, and some important classes of the kernels that satisfy this condition are introduced.
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Time-space variable-order fractional nonlinear system of thermoelasticity: numerical treatment
Advances in Difference Equations, 2020 This paper focuses on a numerical study of the general time-space variable-order fractional nonlinear problem of thermoelasticity in one dimension using the weighted average nonstandard finite difference (WANSFD).
Taghreed A. Assiri
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Nonlinear Engineering, 2023 A nonlinear Boussinesq equation under fractal fractional Caputo’s derivative is studied. The general series solution is calculated using the double Laplace transform with decomposition. The convergence and stability analyses of the model are investigated
Algahtani Obaid J.
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Generalized Fractional Derivative, Fractional differential ring
, 2021 There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there is an infinite number of possible definitions of fractional derivatives, all are correct as differential ...
Toghani, Zeinab, Gaggero, Luis
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New applications of the new general integral transform method with different fractional derivatives
Alexandria Engineering Journal, 2023 Integral transforms are a versatile mathematical technique that can be applied in a wide range of science and engineering fields. We consider the general integral transform with the Caputo derivative and Constant Proportional Caputo derivative in this ...
Ali Akgül +4 more
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