On a solution of a fractional hyper-Bessel differential equation by means of a multi-index special function
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Riccardo Droghei
Abstract
In this paper we introduce a new multiple-parameters (multi-index) extension of the Wright function that arises from an eigenvalue problem for a case of hyper-Bessel operator involving Caputo fractional derivatives. We show that by giving particular values to the parameters involved in this special function, this leads to some known special functions (as the classical Wright function, the α-Mittag-Leffler function, the Tricomi function, etc.) that on their turn appear as cases of the so-called multi-index Mittag-Leffler functions. As an application, we mention that this new generalization Wright function nis an isochronous solution of a nonlinear fractional partial differential equation.
Acknowledgements
The author is grateful to Dr. Roberto Garra for providing essential information, to the Editor who helped to enter this topic in deep, and to expand the bibliography.
References
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© 2021 Diogenes Co., Sofia
Artikel in diesem Heft
- Frontmatter
- Editorial
- FCAA related news, events and books
- Survey Paper
- Towards a unified theory of fractional and nonlocal vector calculus
- Research Paper
- An adaptive memory method for accurate and efficient computation of the Caputo fractional derivative
- Analysis of solutions of some multi-term fractional Bessel equations
- Existence of solutions for the semilinear abstract Cauchy problem of fractional order
- Summability of formal solutions for a family of generalized moment integro-differential equations
- Analysis and fast approximation of a steady-state spatially-dependent distributed-order space-fractional diffusion equation
- Green’s function for the fractional KdV equation on the periodic domain via Mittag–Leffler function
- First order plus fractional diffusive delay modeling: Interconnected discrete systems
- On a solution of a fractional hyper-Bessel differential equation by means of a multi-index special function
- On the decomposition of solutions: From fractional diffusion to fractional Laplacian
- Output error MISO system identification using fractional models
- Short Paper
- Identification of system with distributed-order derivatives
- Short note
- On the Green function of the killed fractional Laplacian on the periodic domain
Artikel in diesem Heft
- Frontmatter
- Editorial
- FCAA related news, events and books
- Survey Paper
- Towards a unified theory of fractional and nonlocal vector calculus
- Research Paper
- An adaptive memory method for accurate and efficient computation of the Caputo fractional derivative
- Analysis of solutions of some multi-term fractional Bessel equations
- Existence of solutions for the semilinear abstract Cauchy problem of fractional order
- Summability of formal solutions for a family of generalized moment integro-differential equations
- Analysis and fast approximation of a steady-state spatially-dependent distributed-order space-fractional diffusion equation
- Green’s function for the fractional KdV equation on the periodic domain via Mittag–Leffler function
- First order plus fractional diffusive delay modeling: Interconnected discrete systems
- On a solution of a fractional hyper-Bessel differential equation by means of a multi-index special function
- On the decomposition of solutions: From fractional diffusion to fractional Laplacian
- Output error MISO system identification using fractional models
- Short Paper
- Identification of system with distributed-order derivatives
- Short note
- On the Green function of the killed fractional Laplacian on the periodic domain