Integrals and derivatives of fractional order based on Laplace type integral transformations with applications
نویسندگان
چکیده
Развивается теория интегралов и производных дробного порядка. Построен аналог операционного исчисления для дифференциального оператора с кусочно-постоянными коэффициентами. Предложены различные конструкции обобщенного преобразования Лапласа. При помощи операторов установлена связь интегральных преобразований Меллина – Лапласа обобщенным интегральным преобразованием Найден изоморфизм пространства оригиналов обобщенных оригиналов. Установлены формулы обращения типа Доказаны теоремы о дифференцировании оригинала другие. Дано определение обобщенной свертки формула ее вычисления, указана классической свертки. На основе понятия дано интеграла производной соотношения между обобщенными интегралами порядка Римана Лиувилля Для модельного уравнения теплопроводности кусочно постоянным коэффициентом решена задача вычисления плотности теплового потока. Тепловой поток выражен в виде 1/2 по времени от измеренной зависимости температуры на границе.
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ژورنال
عنوان ژورنال: Prikladnaâ matematika & fizika
سال: 2021
ISSN: ['2687-0959']
DOI: https://doi.org/10.52575/2687-0959-2021-53-2-114-124