Results 71 to 80 of about 2,487 (168)

A further extension of the extended Riemann–Liouville fractional derivative operator

TURKISH JOURNAL OF MATHEMATICS, 2018
Summary: The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations ...
Martin BOHNER, Gauhar RAHMAN, Shahid MUBEEN, Kottakkaran Sooppy NISAR   +3 more
openaire   +2 more sources

Laplace’s transform of fractional order via the Mittag–Leffler function and modified Riemann–Liouville derivative

, 2009
We propose a (new) definition of a fractional Laplace’s transform, or Laplace’s transform of fractional order, which applies to functions which are fractional differentiable but are not differentiable, in such a manner that they cannot be analyzed by ...
Jumarie, Guy
core   +1 more source

Leibniz rule for riemann-liouville fractional derivative

, 2017
Bu tez beş bölümden oluşmaktadır. Birinci bölümde yapılan çalışmalar ve tezin genel amacı hakkında bilgiler verilmiştir. İkinci bölümde ise Gamma fonksiyonu, Beta fonksiyonu gibi temel kavramlar açıklanmıştır.
Arslan, Sevilay
core  

Analytical approximate solutions of fractionel convection-diffusion equation with modified Riemann-Liouville derivative by means of fractional variational iteration method

, 2013
In this article, an analytical approximate solution of nonlinear fractional convection-diffusion with modified Riemann-Liouville derivative was obtained with the help of fractional variational iteration method (FVIM).
M Merdan
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Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results

, 2006
The paper gives some results and improves the derivation of the fractional Taylor's series of nondifferentiable functions obtained recently in the form f (χ + h) = Eα (hαDχα)f(χ), 0 α ≤ 1, where Eα is the Mittag-Leffier function.
Jumarie, G.
core   +1 more source

Some applications of the multi-dimensional fractional order for the Riemann-Liouville derivative [PDF]

, 2016
In this paper, the aim of this work is to study theorem for the one-dimensional space-time fractional deriative, generalize some function for the one-dimensional fractional by table represents the fractional Laplace transforms of some elementary ...
Ahmood, Wasan Ajeel, Kilicman, Adem, Wasan Ajeel Ahmood, Adem Kiliçman   +3 more
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Generalized Extended Riemann-Liouville type fractional derivative operator

, 2019
In this paper, we aim to present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella hypergeometric functions, by using the extended Bessel function due to Boudjelkha [4].
Abbas, Hafida, Azzouz, Abdelhalim, Zahaf, Mohammed Brahim, Belmekki, Mohamed   +3 more
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Extended Jacobi Functions via Riemann-Liouville Fractional Derivative [PDF]

, 2020
By means of the Riemann-Liouville fractional calculus, extended Jacobi functions are defined and some of their properties are obtained. Then, we compare some properties of the extended Jacobi functions extended Jacobi polynomials.
Esra Erkug-Duman, Bayram Çekim
core  

A Survey on Semilinear Differential Equations and Inclusions Involving Riemann-Liouville Fractional Derivative

, 2009
We establish sufficient conditions for the existence of mild solutions for some densely defined semilinear functional differential equations and inclusions involving the Riemann-Liouville fractional derivative.
Belmekki, Mohammed, Ravi P. Agarwal, Mohammed Belmekki, Mouffak Benchohra, Agarwal, Ravi P., Benchohra, Mouffak   +5 more
core   +1 more source

Regularity of mild solutions to fractional Cauchy problems with Riemann-Liouville fractional derivative

, 2014
As an extension of the fact that a sectorial operator can determine an analytic semigroup, we first show that a sectorial operator can determine a real analytic alpha-order fractional resolvent which is defined in terms of Mittag-Leffler function and ...
Hong-Rui Sun, Ya-Ning Li
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