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19 results on '"Luchko, Yu."'

4. On an extension of the Mikusiński type operational calculus for the Caputo fractional derivative.

Author

Al-Kandari, M., Hanna, L. A-M., and Luchko, Yu.

Subjects
CAPUTO fractional derivatives, FRACTIONAL calculus, HOMOMORPHISMS, CALCULUS
Abstract

In this paper, a two-parameter extension of the operational calculus of Mikusiński's type for the Caputo fractional derivative is presented. The first parameter is connected with the rings of functions that are used as a basis for construction of the convolution quotients fields. The convolutions by themselves are characterized by another parameter. The obtained two-parameter operational calculi are compared each to other and some homomorphisms between the fields of convolution quotients are established. [ABSTRACT FROM AUTHOR]

Published
2021
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5. Algorithms for the Fractional Calculus: A Selection of Numerical Methods

Author

Diethelm, K, Ford, N. J, Freed, A. D, and Luchko, Yu

Subjects
Numerical Analysis
Abstract

Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.

Published
2003

10. Double computation schemes of solution unlinear integro-partial differential equations with the main error estimation

Author

Pelekh, R. Ya. and Luchko, Yu. Yu.

Subjects
нелинейные дифференциальные уравнения, погрешность, метод Рунге-Кутта, ряд Тейлора, нелінійні диференціальні рівняння, похибка, nonlinear differential equations, precision error, Runge-Kutta method, Taylor series
Abstract

Виведено двосторонні розрахункові формули другого порядку точності розв’язання задачі Коші для звичайних диференціальних рівнянь, що базуються на неперервних дробах. У запропонованих обчислювальних формулах можна оцінити значення головного члена локальної похибки без додаткових звертань до правої частини диференціального рівняння., Выведены двусторонние расчетные формулы второго порядка точности решения задачи Коши для обычных дифференциальных уравнений, которые базируются на непрерывных дробях. В предложенных вычислительных формулах можно оценить значение главного члена локальной погрешности без дополнительных обращений к правой части дифференциального уравнения., The two-side methods of the second order of accuracy are constructed. The formulas give an opportunity to receive upper and lover approximation at each point to the exact solution and define the value of the main error without referring to the right part of differential equation.

Published
2011

17. The generalizations of integral analog of the Leibniz rule on the G-convolutions

Author

Yakubovich, Semen B., Luchko, Yu F., Yakubovich, Semen B., and Luchko, Yu F.

Abstract

An integral analog of the Leibniz rule for the operators of fractional calculus was considered in paper [1]. These operators are known to belong to the class of convolution transforms [2]. It seems very natural to try to obtain some new integral analog of the Leibniz rule for other convolution operators. We have found a general method for constructing such integral analogs on the base of notion of G-convolution [4]. Several results obtained by this method are represented in this article

Published
1991

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