О Полноте Систем Корневых Функций Дифференциального Оператора Дробного Порядка С Матричными Коэффициентами

Agibalova, Anna V.

doi:10.4213/mzm8806

Mat. Zametki

2010

DOI: 10.4213/mzm8806

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О Полноте Систем Корневых Функций Дифференциального Оператора Дробного Порядка С Матричными Коэффициентами

Anna V. Agibalova¹

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Boundary-value problems for differential equations of fractional order

2013

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Abstract. We carry out spectral analysis of one class of integral operators associated with fractional order differential equations that arise in mechanics. We establish a connection between the eigenvalues of these operators and the zeros of Mittag-Leffler type functions. We give sufficient conditions for complete nonselfadjointness and completeness of systems of the eigenvalues. We prove the existence and uniqueness of the solutions for several kinds of two-point boundary value problems of fractional differential equations with Caputo's derivatives or Riemann-Liouville Derivatives, and design the single shooting methods to solve them numerically.Chapter 1. Regional problems for differential equations of fractional order 1. The basic concepts The spectral analysis of operators of the form

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Boundary-value problems for differential equations of fractional order

2013

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The analysis of the polymer concrete characteristics by fractional calculus

Aleroev

2019

J. Phys.: Conf. Ser.

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The paper investigates a second-order differential equation with a fractional derivative in the lower term, in which the order of the fractional derivative is in the range from zero to two and is not known in advance. This model is used to describe oscillatory processes in a viscous medium. A fundamentally new method has been developed for the approximate solution of the first boundary-value problem for the equation of string vibration taking into account friction in a medium with fractal geometry. Considering that polymer concrete is a set of granules of a mineral filler located in a viscous medium, the equation of motion of these granules is derived and investigated. A technique is proposed for studying the motion of granules in a medium with fractal geometry.

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The problem of finding the radon flux density by its concentration at different depths of the earth’s surface

Aleroev

Erokhin

2019

J. Phys.: Conf. Ser.

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О Полноте Систем Корневых Функций Дифференциального Оператора Дробного Порядка С Матричными Коэффициентами

Cited by 4 publications

References 0 publications

Boundary-value problems for differential equations of fractional order

Boundary-value problems for differential equations of fractional order

The analysis of the polymer concrete characteristics by fractional calculus

The problem of finding the radon flux density by its concentration at different depths of the earth’s surface

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