Results 31 to 40 of about 2,558 (225)

Degenerate Linear Evolution Equations with the Riemann–Liouville Fractional Derivative

Siberian Mathematical Journal, 2018
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Fedorov, V. E., Plekhanova, M. V., Nazhimov, R. R.   +2 more
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A new Riemann–Liouville type fractional derivative operator and its application in generating functions

Advances in Difference Equations, 2018
Here, the concept of a new and interesting Riemann–Liouville type fractional derivative operator is exploited. Treatment of a fractional derivative operator has been made associated with the extended Appell hypergeometric functions of two variables and ...
M. Shadab, M. Faisal Khan, J. Luis Lopez-Bonilla   +2 more
doaj   +1 more source

Analysis of nonlinear fractional diffusion equations with a Riemann-liouville derivative

Evolution Equations & Control Theory, 2022
<p style='text-indent:20px;'>In this paper, we consider a nonlinear fractional diffusion equations with a Riemann-Liouville derivative. First, we establish the global existence and uniqueness of mild solutions under some assumptions on the input data.
Ngoc, Tran Bao, Tuan, Nguyen Huy, Sakthivel, R., O'Regan, Donal   +3 more
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Fractional Cauchy Problem with Riemann-Liouville Derivative on Time Scales [PDF]

Abstract and Applied Analysis, 2013
Summary: \(\nabla\)-Laplace transform, fractional \(\nabla\)-power function, \(\nabla\)-Mittag-Leffler function, fractional \(\nabla\)-integrals, and fractional \(\nabla\)-differential on time scales are defined. Some of their properties are discussed in detail.
Ling Wu, Jiang Zhu
openaire   +3 more sources

Integral-Type Fractional Equations with a Proportional Riemann–Liouville Derivative [PDF]

Journal of Mathematics, 2021
In this paper, we present the necessary conditions where integral-type fractional equations with a proportional Riemann–Liouville derivative have a unique solution. Also, we give an example to illustrate our work.
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Extension of the fractional derivative operator of the Riemann-Liouville

The Journal of Nonlinear Sciences and Applications, 2017
Summary: By using the generalized beta function, we extend the fractional derivative operator of the Riemann-Liouville and discusses its properties. Moreover, we establish some relations to extended special functions of two and three variables via generating functions.
Baleanu, Dumitru, Agarwal, Praveen, Parmar, Rakesh K., Alqurashi, Maysaa M., Salahshour, Soheil   +4 more
openaire   +3 more sources

Sequential generalized Riemann–Liouville derivatives based on distributional convolution

Fractional Calculus and Applied Analysis, 2022
Abstract Sequential generalized fractional Riemann–Liouville derivatives are introduced as composites of distributional derivatives on the right half axis and partially defined operators, called Dirac-function removers, that remove the component of singleton support at the origin of distributions that are of order zero on a neighborhood ...
Kleiner, Tillmann, Hilfer, Rudolf
openaire   +2 more sources

Sturm-Liouville Problem with Mixed Boundary Conditions for a Differential Equation with a Fractional Derivative and Its Application in Viscoelasticity Models

Axioms, 2023
In this study, we obtained a system of eigenfunctions and eigenvalues for the mixed homogeneous Sturm-Liouville problem of a second-order differential equation containing a fractional derivative operator.
Ludmila Kiryanova, Tatiana Matseevich
doaj   +1 more source

A highly accurate numerical method for solving boundary value problem of generalized Bagley‐Torvik equation

Mathematical Methods in the Applied Sciences, EarlyView.
A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay, Mtema James Chin, Nazim I. Mahmudov   +2 more
wiley   +1 more source

Riemann–Liouville Fractional Calculus of Nonlinear Hidden Variable Recurrent Fractal Interpolation Functions Based on Rakotch Contraction

Journal of Function Spaces
In this paper, we study Riemann–Liouville fractional calculus of nonlinear hidden variable recurrent fractal interpolation function (HVRFIF) constructed based on Rakotch contraction, which is a generalization of Banach contraction.
Chung-Il Ro, Chol-Hui Yun, Song-Chol Kwon, Un-Ryong Rim   +3 more
doaj   +1 more source