Abstract
In this paper, we first address the general fractional integrals and derivatives with the Sonine kernels that possess the integrable singularities of power function type at the point zero. Both particular cases and compositions of these operators are discussed. Then we proceed with a construction of an operational calculus of the Mikusiński type for the general fractional derivatives with the Sonine kernels. This operational calculus is applied for analytical treatment of some initial value problems for the fractional differential equations with the general fractional derivatives. The solutions are expressed in form of the convolution series that generalize the power series for the exponential and the Mittag-Leffler functions.
Dedicated to Professor Stefan Samko on the occasion of his 80th birthday
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© 2021 Diogenes Co., Sofia
Artikel in diesem Heft
- Frontmatter
- Editorial Note
- Anniversary of Prof. S.G. Samko, FC Events (FCAA–Volume 24–2–2021)
- Research Paper
- Operational calculus for the general fractional derivative and its applications
- Riesz potentials and orthogonal radon transforms on affine Grassmannians
- Characterizations of variable martingale Hardy spaces via maximal functions
- Survey Paper
- Contributions on artificial potential field method for effective obstacle avoidance
- Research Paper
- Self-similar cauchy problems and generalized Mittag-Leffler functions
- Asymptotic behavior of solutions of fractional differential equations with Hadamard fractional derivatives
- A boundary value problem for a partial differential equation with fractional derivative
- Operational calculus for the Riemann–Liouville fractional derivative with respect to a function and its applications
- Duality theory of fractional resolvents and applications to backward fractional control systems
- Kinetic solutions for nonlocal stochastic conservation laws
- A fractional analysis in higher dimensions for the Sturm-Liouville problem
- Averaging theory for fractional differential equations
Artikel in diesem Heft
- Frontmatter
- Editorial Note
- Anniversary of Prof. S.G. Samko, FC Events (FCAA–Volume 24–2–2021)
- Research Paper
- Operational calculus for the general fractional derivative and its applications
- Riesz potentials and orthogonal radon transforms on affine Grassmannians
- Characterizations of variable martingale Hardy spaces via maximal functions
- Survey Paper
- Contributions on artificial potential field method for effective obstacle avoidance
- Research Paper
- Self-similar cauchy problems and generalized Mittag-Leffler functions
- Asymptotic behavior of solutions of fractional differential equations with Hadamard fractional derivatives
- A boundary value problem for a partial differential equation with fractional derivative
- Operational calculus for the Riemann–Liouville fractional derivative with respect to a function and its applications
- Duality theory of fractional resolvents and applications to backward fractional control systems
- Kinetic solutions for nonlocal stochastic conservation laws
- A fractional analysis in higher dimensions for the Sturm-Liouville problem
- Averaging theory for fractional differential equations