Operational method for solving fractional differential equations with the left-and right-hand sided Erdélyi-Kober fractional derivatives

DOI10.1515/fca-2020-0004zbMath1441.34009OpenAlexW3007669355MaRDI QIDQ2176137

Yuri Luchko, Maryam Al-Kandari, L. A.-M. Hanna

Publication date: 4 May 2020

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/fca-2020-0004

zbMATH Keywords

integral transformsfractional differential equationsconvolutionsoperational methodcomposed Erdélyi-Kober integrals and derivativesleft-and right-hand sided Erdélyi-Kober derivativesleft-and right-hand sided Erdélyi-Kober integralsWright type functions

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Fractional derivatives and integrals (26A33) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Other functions coming from differential, difference and integral equations (33E30) Fractional ordinary differential equations (34A08) Integro-ordinary differential equations (45J99) Volterra integral equations (45D99)

Related Items (6)

On a variant of multivariate Mittag-Leffler's function arising in the Laplace transform method ⋮ Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems ⋮ Analysis of fractional integro-differential equations with nonlocal Erdélyi-Kober type integral boundary conditions ⋮ Erdélyi-Kober fractional integrals and Radon transforms for mutually orthogonal affine planes ⋮ Operational calculus for the Riemann-Liouville fractional derivative with respect to a function and its applications ⋮ On fractional calculus with analytic kernels with respect to functions

Cites Work

• Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
• An operational method for solving fractional differential equations with the Caputo derivatives
• Wright functions as scale-invariant solutions of the diffusion-wave equation
• The exact solution of certain differential equations of fractional order by using operational calculus
• The Multi-index Mittag-Leffler Functions and Their Applications for Solving Fractional Order Problems in Applied Analysis
• Operationl method for solving generalized abel integral equation of second kind
• Basic Theory
• A convolution family in the Dimovski sense for the composed Erdélyi-Kober fractional integrals
• Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation
• Erdélyi-Kober fractional diffusion
• Operational calculus for the Caputo-type fractional Erdélyi–Kober derivative and its applications
• The Asymptotic Expansion of the Generalized Hypergeometric Function
• Un théorème sur le produit de composition des fonctions de plusieurs variables
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