Results 11 to 20 of about 14,096 (164)
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.
Yuri Luchko
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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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Generalized Taylor’s formula for power fractional derivatives
Boletín de la Sociedad Matemática Mexicana, 2023 AbstractWe establish a new generalized Taylor’s formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor’s formulas in the literature. Moreover, as a consequence, we obtain a general version of the classical mean value theorem.
Hanaa Zitane, Delfim F. M. Torres
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Scale-Invariant General Fractional Calculus: Mellin Convolution Operators
Fractal and Fractional, 2023 General fractional calculus (GFC) of operators that is defined through the Mellin convolution instead of Laplace convolution is proposed. This calculus of Mellin convolution operators can be considered as an analogue of the Luchko GFC for the Laplace ...
Vasily E. Tarasov
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On the 1st-Level General Fractional Derivatives of Arbitrary Order
Fractal and Fractional, 2023 In this paper, the 1st-level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and ...
Yuri Luchko
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An Efficient Method for Solving [PDF]
Kirkuk Journal of Science, 2008 This paper presents a new method for solving fractional partial differential equations (FPDE) which is called the polynomial approximation method based on the polynomial approximation uN(x,t) and on its general fractional derivative formula.By modifying ...
Omar M. Al-Faour
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Taylor’s formula involving generalized fractional derivatives [PDF]
Applied Mathematics and Computation, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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Study of generalized type K-fractional derivatives [PDF]
Advances in Difference Equations, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Azam, M. K., Farid, G., Rehman, M. A.
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