► Fuzzy fractional H-differentiability is provided. ► The fuzzy Laplace transform of fuzzy fractional derivatives is obtained. ► Some new basic properties of fuzzy Laplace transforms are derived. ► ...Fuzzy fractional differential equations is solved using mentioned method.
This paper deals with the solutions of fuzzy fractional differential equations (FFDEs) under Riemann–Liouville H-differentiability by fuzzy Laplace transforms. In order to solve FFDEs, it is necessary to know the fuzzy Laplace transform of the Riemann–Liouville H-derivative of
f,
RL
D
a
+
β
f
(
x
)
. The virtue of
L
RL
D
a
+
β
f
(
x
)
is that can be written in terms of
L
f(
x). Moreover, some illustrative examples are solved to show the efficiency and utility of Laplace transforms method.
The analysis of the behaviors of physical phenomena is important to discover significant features of the character and the structure of mathematical models. Frequently the unknown parameters involve ...in the models are assumed to be unvarying over time. In reality, some of them are uncertain and implicitly depend on several factors. In this study, to consider such uncertainty in variables of the models, they are characterized based on the fuzzy notion. We propose here a new model based on fractional calculus to deal with the Kelvin–Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters. A new and accurate numerical algorithm using a spectral tau technique based on the generalized fractional Legendre polynomials (GFLPs) is developed to solve those problems under uncertainty. Numerical simulations are carried out and the analysis of the results highlights the significant features of the new technique in comparison with the previous findings. A detailed error analysis is also carried out and discussed.
In this relativistic consideration, the energy integral unlike others has been derived in a weakly relativistic plasma in terms of Sagdeev potential. Both compressive and rarefactive subsonic ...solitary waves are found to exist, depending on wave speeds in various directions of propagation. It is found that compressive relativistic solitons have potential depths that are higher than non-relativistic solitons in all directions of propagation, allowing for the presence of denser plasma particles in the potential well. Furthermore, it shows how compressive soliton amplitude grows as the propagation direction gets closer to the magnetic field’s direction.
The main aim of this paper is to conduct a detailed study on a high-order nonlinear Schrödinger (HONLS) equation involving nonlinear dispersions and the Kerr effect. More precisely, after reducing ...the governing model describing ultra-short pulses in optical fibers in a one-dimensional domain, its optical solitons including the bright and dark solitons are derived through the modified Kudryashov (MK) method. The dynamical behavior of the bright and dark solitons is formally investigated for different sets of the involved parameters. It is shown that increasing and decreasing nonlinear dispersions lead to significant changes in the amplitude of the bright and dark solitons.
We give the explicit solutions of uncertain fractional differential equations (UFDEs) under Riemann–Liouville
H
-differentiability using Mittag-Leffler functions. To this end, Riemann–Liouville
H
...-differentiability is introduced which is a direct generalization of the concept of Riemann–Liouville differentiability in deterministic sense to the fuzzy context. Moreover, equivalent integral forms of UFDEs are determined which are applied to derive the explicit solutions. Finally, some illustrative examples are given.
The major goal of the current paper is to conduct a detailed study on a generalized KdV equation (gKdVE) and its non-singular multi-complexiton wave. More precisely, first the multi-shock wave of the ...governing model is retrieved using the principle of linear superposition. Based on the multi-shock wave and the techniques adopted by Zhou and Manukure, the non-singular multi-complexiton wave to the gKdVE is then constructed with the help of symbolic computations. The dynamical properties of single and double shock waves as well as non-singular single and double complexiton waves are analyzed by representing a group of 3D-plots. The achievements of the present paper take an important step in completing the research on the generalized KdV equation.
The Oil Palm Frond (a lignocellulosic material) is a high-yielding energy crop that can be utilized as a promising source of xylose. It holds the potential as a feedstock for bioethanol production ...due to being free and inexpensive in terms of collection, storage and cropping practices. The aim of the paper is to calculate the concentration and yield of xylose from the acid hydrolysis of the Oil Palm Frond through a fuzzy fractional kinetic model. The approximate solution of the derived fuzzy fractional model is achieved by using a tau method based on the fuzzy operational matrix of the generalized Laguerre polynomials. The results validate the effectiveness and applicability of the proposed solution method for solving this type of fuzzy kinetic model.
•A new fractional kinetic equation under uncertainty was addressed to depict the chemical reaction arising in Palm Oil Frond.•An efficient numerical simulation based on a tau method was derived to solve the proposed kinetic equation.•Different cases were solved to demonstrate the validity and efficiency of the proposed technique.
This paper deals with the solutions of fuzzy Volterra integral equations with separable kernel by using fuzzy differential transform method (FDTM). If the equation considered has a solution in terms ...of the series expansion of known functions, this powerful method catches the exact solution. To this end, we have obtained several new results to solve mentioned problem when FDTM has been applied. In order to show this capability and robustness, some fuzzy Volterra integral equations are solved in detail as numerical examples.
In this paper, a novel coronavirus infection system with a fuzzy fractional differential equation defined in Caputo’s sense is developed. By using the fuzzy Laplace method coupled with Adomian ...decomposition transform, numerical results are obtained for better understanding of the dynamical structures of the physical behavior of COVID-19. Such behavior on the general properties of RNA in COVID-19 is also investigated for the governing model. The results demonstrate the efficiency of the proposed approach to address the uncertainty condition in the pandemic situation.
Fractional calculus is an important branch of mathematical analysis and played a fundamental role in different fields including signal processing and image processing. In this paper, we proposed a ...sparse super-resolution (SR) technique by using the Grünwald-Letnikov (G–L) fractional differential operator, which aims to reconstruct high-resolution images by recovering pixel information from low-resolution images. We suggested a modified fractional derivative mask based on G–L for image enhancement. The proposed method suppresses block artifacts, staircase edges, and false edges near the edges. The proposed method is very flexible and preserves detailed features. The obtained experiments demonstrated that fractional operator can nonlinearly preserve the low-frequency contour information in the smooth region and also nonlinearly improve well the high-frequency edge and texture of the image. In sparse SR images, the dictionary is constructed by texture information of the images by using integer derivatives. In this work, we computed dictionary matrices by applying the fractional masks. In fact, the extracted features based on fractional derivatives are utilized in the dictionary training procedure and sparse coding. The experimental results and analysis on natural images indicated that the proposed method achieved much better results than other algorithms in terms of both quantitative measures and visual perception.
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