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 …
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 …
variation of Chebyshev differential equations is introduced based on Caputo fractional …
On linear fractional differential equations with variable coefficients
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 …
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 …
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 …
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 …
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 …
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 …
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 …
equation. We replace the integer derivative by the conformable derivative of order 0< α< 1 …
[PDF][PDF] Hilfer fractional spectral problem via Bessel operator
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 …
potential and we show the self-adjointness of the operator, orthogonality of distinct …