Approximation of the Erdélyi--Kober operator with application to the time-fractional Porous medium equation

Ł Płociniczak - SIAM journal on applied mathematics, 2014 - SIAM
This paper describes a method of approximating equations with the Erdélyi--Kober fractional
operator which arise in mathematical descriptions of anomalous diffusion. We prove a …

On the analysis and design of fractional-order chebyshev complex filter

AM AbdelAty, A Soltan, WA Ahmed… - Circuits, Systems, and …, 2018 - Springer
This paper introduces the concept of fractional-order complex Chebyshev filter. A fractional
variation of Chebyshev differential equations is introduced based on Caputo fractional …

On linear fractional differential equations with variable coefficients

A Fernandez, JE Restrepo, D Suragan - Applied Mathematics and …, 2022 - Elsevier
We study and solve linear ordinary differential equations, with fractional order derivatives of
either Riemann–Liouville or Caputo types, and with variable coefficients which are either …

Analysis of solutions of some multi-term fractional Bessel equations

PB Dubovski, J Slepoi - Fractional Calculus and Applied Analysis, 2021 - degruyter.com
We construct the existence theory for generalized fractional Bessel differential equations
and find the solutions in the form of fractional or logarithmic fractional power series. We …

Construction and analysis of series solutions for fractional quasi-Bessel equations

PB Dubovski, JA Slepoi - Fractional Calculus and Applied Analysis, 2022 - Springer
In this paper we introduce fractional quasi-Bessel equations∑ i= 1 mdix ξ i D α iu (x)+(x β-ν
2) u (x)= 0 and construct their existence theory in the class of fractional series solutions. In …

Existence and linear independence theorem for linear fractional differential equations with constant coefficients

PB Dubovski, JA Slepoi - Journal of Applied Analysis, 2024 - degruyter.com
We consider the l-th order linear fractional differential equations with constant coefficients.
Here l∈ ℕ is the ceiling for the highest derivative of order α, l-1< α≤ l. If β i< α are the other …

On finite fractional Sturm–Liouville transforms

A Ansari - Integral Transforms and Special Functions, 2015 - Taylor & Francis
In this article, we introduce the finite fractional Sturm–Liouville transforms for the four classes
of fractional operators involving the left-sided and right-sided Riemann–Liouville, Caputo …

Eigenvalue asymptotics for a fractional boundary-value problem

Ł Płociniczak - Applied Mathematics and Computation, 2014 - Elsevier
This letter presents a result concerning eigenvalue approximation of a boundary-value
problem with the Caputo fractional derivative. This approximation is derived by the use of the …

The fractional Laguerre equation: series solutions and fractional Laguerre functions

R Shat, S Alrefai, I Alhamayda, A Sarhan… - Frontiers in Applied …, 2019 - frontiersin.org
In this paper, we propose a fractional generalization of the well-known Laguerre differential
equation. We replace the integer derivative by the conformable derivative of order 0< α< 1 …

[PDF][PDF] Hilfer fractional spectral problem via Bessel operator

E Panakhov, A Ercan, E Bas, R Ozarslan - TWMS J Pure Appl Math, 2019 - static.bsu.az
In this paper, we deal with a modified fractional Hilfer Sturm–Liouville operator for Bessel
potential and we show the self-adjointness of the operator, orthogonality of distinct …