Journal
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
Volume 23, Issue 1, Pages 103-125Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/fca-2020-0004
Keywords
operational method; fractional differential equations; left- and right-hand sided Erdelyi-Kober integrals; left- and right-hand sided Erdelyi-Kober derivatives; composed Erdelyi-Kober integrals and derivatives; convolutions; integral transforms; Wright type functions
Funding
- Kuwait University [SM02/18]
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In this paper, we first provide a survey of some basic properties of the left- and right-hand sided Erd ' elyi-Kober fractional integrals and derivatives and introduce their compositions in form of the composed Erdelyi-Kober operators. Then we derive a convolutional representation for the composed Erdelyi-Kober fractional integral in terms of its convolution in the Dimovski sense. For this convolution, we also determine the divisors of zero. These both results are then used for construction of an operational method for solving an initial value problem for a fractional differential equation with the left- and right-hand sided Erdelyi-Kober fractional derivatives defined on the positive semi-axis. Its solution is obtained in terms of the four-parameters Wright function of the second kind. The same operational method can be employed for other fractional differential equation with the left- and right-hand sided Erdelyi-Kober fractional derivatives.
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