Browsing by Author "Atangana, Abdon"

Now showing 1 - 19 of 19

Citation - WoS: 49
Citation - Scopus: 58
A Numerical Schemes and Comparisons for Fixed Point Results With Applications to the Solutions of Volterra Integral Equations in Dislocatedextendedb-Metricspace
(Elsevier, 2020) Panda, Sumati Kumari; Karapınar, Erdal; Karapinar, Erdal; Atangana, Abdon; Matematik
In this article, we propose a generalization of both b-metric and dislocated metric, namely, dislocated extended b-metric space. After getting some fixed point results, we suggest a relatively simple solution for a Volterra integral equation by using the technique of fixed point in the setting of dislocated extended b-metric space. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
Citation - WoS: 224
Analysis of time-fractional Hunter-Saxton equation: a model of neumatic liquid crystal
(Sciendo, 2016) Atangana, Abdon; Baleanu, Dumitru; Baleanu, Dumitru; Alsaedi, Ahmed; 56389; Matematik
In this work, a theoretical study of diffusion of neumatic liquid crystals was done using the concept of fractional order derivative. This version of fractional derivative is very easy to handle and obey to almost all the properties satisfied by the conventional Newtonian concept of derivative. The mathematical equation underpinning this physical phenomenon was solved analytically via the so-called homotopy decomposition method. In order to show the accuracy of this iteration method, we constructed a Hilbert space in which we proved its stability for the time-fractional Hunder-Saxton equation.
Citation - WoS: 24
Application of Fixed Point Theorem for Stability Analysis of a Nonlinear Schrodinger with Caputo-Liouville Derivative
(Univ Nis, Fac Sci Math, 2017) Atangana, Abdon; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
Using the new Caputo-Liouville derivative with fractional order, we have modified the nonlinear Schrdinger equation. We have shown some useful in connection of the new derivative with fractional order. We used an iterative approach to derive an approximate solution of the modified equation. We have established the stability of the iteration scheme using the fixed point theorem. We have in addition presented in detail the uniqueness of the special solution.
Citation - WoS: 251
Citation - Scopus: 267
Caputo-Fabrizio derivative applied to groundwater flow within confined aquifer
(Asce-amer Soc Civil Engineers, 2017) Atangana, Abdon; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
The model of the movement of subsurface water via the geological formation called aquifer was extended using a newly proposed derivative with fractional order. An alternative derivative to that of Caputo-Fabrizio with fractional order was presented. The relationship between both derivatives was presented. The new equation was solved analytically using some integral transforms. The exact solution is therefore compared to experimental data obtained from the settlement of the University of the Free State in South Africa. The numerical simulation shows the agreement of the experimental data with an analytical solution for some values of fractional order. (C) 2016 American Society of Civil Engineers.
Citation - WoS: 0
Contemporary Modelling Methods in Heat, Mass, And Fluid Flow - Second Part
(Vinca inst Nuclear Sci, 2017) Hristov, Jordan; Baleanu, Dumitru; Baleanu, Dumitru; Atangana, Abdon; 56389; Matematik
Citation - WoS: 0
From The Guest Editors Contemporary Modelling Methods in Heat, Mass, And Fluid Flow Special Collection Of Articles
(Vinca inst Nuclear Sci, 2017) Hristov, Jordan; Baleanu, Dumitru; Baleanu, Dumitru; Atangana, Abdon; 56389; Matematik
Citation - WoS: 14
Modelling the advancement of the impurities and the melted oxygen concentration within the scope of fractional calculus
(Pergamon-elsevier Science Ltd, 2014) Atangana, Abdon; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
The model describing the mitigation of contamination through ventilation inside a moving waterway polluted via dispersed bases together with connected reduction of liquefied oxygen was investigated within the scope of fractional derivatives. The steady-state cases were investigated using some Caputo derivatives properties. The steady-state solutions in presence and absence of the dispersion were derived in terms of the Mittag-Leffler function. In the case of non-steady state, we derived the solution of the first equation in terms of the a-stable error function via the Laplace transform method. To solve the second equation, we constructed the fractional Green function via the Laplace, Fourier and Mellin transforms. The fractional Green function was expressed by mean of the H-function. Particularly, we presented the selected numerical results a function of distance and a. (C) 2014 Elsevier Ltd. All rights reserved.
Citation - WoS: 82
Citation - Scopus: 96
New Fractional Derivatives Applied to the Korteweg-De Vries and Korteweg-De Vries-Burger's Equations
(Springer Heidelberg, 2018) Saad, Khaled M.; Baleanu, Dumitru; Baleanu, Dumitru; Atangana, Abdon; 56389; Matematik
In this paper, we extend the model of the Korteweg-de Vries (KDV) and Korteweg-de Vries-Burger's (KDVB) to new model time fractional Korteweg-de Vries (TFKDV) and time fractional Korteweg-de Vries-Burger's (TFKDVB) with Liouville-Caputo (LC), Caputo-Fabrizio (CF), and Atangana-Baleanu (AB) fractional time derivative equations, respectively. We utilize the q-homotopy analysis transform method (q-HATM) to compute the approximate solutions of TFKDV and TFKDVB using LC, CF and AB in Liouville-Caputo sense. We study the convergence analysis of q-HATM by computing the Residual Error Function (REF) and finding the interval of the convergence through the h-curves. Also, we find the optimal values of h so that, we assure the convergence of the approximate solutions. The results are very effective and accurate in solving the TFKDV and TFKDVB.
Citation - WoS: 2945
Citation - Scopus: 3052
New fractional derivatives with non-local and non-singular kernel theory and application to heat transfer model
(Vinca inst Nuclear Sci, 2016) Atangana, Abdon; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
In this paper a new fractional derivative with non-local and no-singular kernel is proposed. Some useful properties of the new derivative are presented and applied to solve the fractional heat transfer model.
Citation - WoS: 126
Citation - Scopus: 126
New Fractional Derivatives With Non-Singular Kernel Applied to the Burgers Equation
(Amer inst Physics, 2018) Saad, Khaled M.; Baleanu, Dumitru; Atangana, Abdon; Baleanu, Dumitru; 56389; Matematik
In this paper, we extend the model of the Burgers (B) to the new model of time fractional Burgers (TFB) based on Liouville-Caputo (LC), Caputo-Fabrizio (CF), and Mittag-Leffler (ML) fractional time derivatives, respectively. We utilize the Homotopy Analysis Transform Method (HATM) to compute the approximate solutions of TFB using LC, CF, and ML in the Liouville-Caputo sense. We study the convergence analysis of HATM by computing the interval of the convergence, the residual error function (REF), and the average residual error (ARE), respectively. The results are very effective and accurate. Published by AIP Publishing.
Citation - WoS: 18
Citation - Scopus: 19
New Optical Solitons of Fractional Nonlinear Schrodinger Equation With the Oscillating Nonlinear Coefficient: a Comparative Study
(Elsevier, 2022) Jarad, Fahd; Atangana, Abdon; Jahngeer, Adil; Jarad, Fahd; Awrejcewicz, Jan; Matematik
In this current exploration, some new optical soliton structures of fractional nonlinear Schrodinger equation with the oscillating nonlinear coefficient are constructed with three different definitions of fractional operators beta, Riemann-Liouville, and M-Truncated derivatives. These structures are computed with the help of the new auxiliary equation method. This method gives the new analytical solutions of the considered model. The analysis is done by considering the different definitions of the derivatives like Beta, Riemann-Liouville (RL), and M-Truncated derivatives. The considered equation is converted to an ordinary differential equation (ODE) by the use of this complex transformation. The graphical explanation of some obtained results is also elaborated in detail. This work is new and does not exist in literature.
Citation - WoS: 406
New properties of conformable derivative
(de Gruyter Poland Sp Zoo, 2015) Atangana, Abdon; Baleanu, Dumitru; Baleanu, Dumitru; Alsaedi, Ahmed; 56389; Matematik
Recently, the conformable derivative and its properties have been introduced. In this work we have investigated in more detail some new properties of this derivative and we have proved some useful related theorems. Also, some new definitions have been introduced.
Citation - WoS: 25
Citation - Scopus: 39
Nonlinear Fractional Jaulent-Miodek and Whitham-Broer-Kaup Equations Within Sumudu Transform
(Hindawi Ltd, 2013) Atangana, Abdon; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
We solve the system of nonlinear fractional Jaulent-Miodek and Whitham-Broer-Kaup equations via the Sumudu transform homotopy method (STHPM). The method is easy to apply, accurate, and reliable.
Citation - WoS: 32
Citation - Scopus: 41
Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes
(Hindawi Ltd, 2013) Atangana, Abdon; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
A kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. Therefore, we presented the numerical solution via the explicit and the implicit schemes. We presented together the stability and convergence of this time-fractional parabolic equation with two difference schemes. The explicit and the implicit schemes in this case are stable under some conditions.
Citation - WoS: 24
Citation - Scopus: 29
On a more general fractional integration by parts formulae and applications
(Elsevier, 2019) Abdeljawad, Thabet; Abdeljawad, Thabet; Atangana, Abdon; Jarad, Fahd; Gomez-Aguilar, J. F.; Jarad, Fahd; 234808; Matematik
The integration by part comes from the product rule of classical differentiation and integration. The concept was adapted in fractional differential and integration and has several applications in control theory. However, the formulation in fractional calculus is the classical integral of a fractional derivative of a product of a fractional derivative of a given function f and a function g. We argue that, this formulation could be done using only fractional operators: thus, we develop fractional integration by parts for fractional integrals, Riemann-Liouville, Liouville-Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional derivatives. We allow the left and right fractional integrals of order alpha > 0 to act on the integrated terms instead of the usual integral and then make use of the fractional type Leibniz rules to formulate the integration by parts by means of new generalized type fractional operators with binomial coefficients defined for analytic functions. In the case alpha = 1, our formulae of fractional integration by parts results in previously obtained integration by parts in fractional calculus. The two disciplines or branches of mathematics are built differently, while classical differentiation is built with the concept of rate of change of a given function, a fractional differential operator is a convolution. (C) 2019 Elsevier B.V. All rights reserved.
Citation - WoS: 6
Citation - Scopus: 6
On modeling the groundwater flow within a confined aquifer
(Editura Acad Romane, 2015) Atangana, Abdon; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
The groundwater flow equation is used to simulate the movement of water under the confined aquifer. In this paper we study a modification of the groundwater flow equation within a newly proposed derivative. We numerically solve the generalized groundwater flow equation with the Crank-Nicholson scheme. We also analytically solve the generalized equation via the method of separation of variable.
Citation - WoS: 2
Citation - Scopus: 2
On the Nonlinear Perturbation K(n, m) Rosenau-Hyman Equation: A Model of Nonlinear Scattering Wave
(Hindawi Ltd, 2015) Atangana, Abdon; Baleanu, Dumitru; Baleanu, Dumitru; Al Qurashi, Maysaa' Mohamed; Yang, Xiao-Jun; 56389; Matematik
We investigate a nonlinear wave phenomenon described by the perturbation K(m, n) Rosenau-Hyman equation within the concept of derivative with fractional order. We used the Caputo fractional derivative and we proposed an iteration method in order to find a particular solution of the extended perturbation equation. We proved the stability and the convergence of the suggested method for solving the extended equation without any restriction on (m, n) and also on the perturbations terms. Using the inner product we proved the uniqueness of the special solution. By choosing randomly the fractional orders and m, we presented the numerical solutions.
Citation - WoS: 6
Citation - Scopus: 7
Pata type contractions involving rational expressions with an application to integral equations
(Amer inst Mathematical Sciences-aims, 2021) Karapinar, Erdal; Karapınar, Erdal; Atangana, Abdon; Fulga, Andreea; 19184; Matematik
In this paper, we introduce the notion of rational Pata type contraction in the complete metric space. After discussing the existence and uniqueness of a fixed point for such contraction, we consider a solution for integral equations.
Citation - WoS: 9
Citation - Scopus: 13
Thermal and Concentration Diffusion Impacts on Mhd Maxwell Fluid: a Generalized Fourier's and Fick's Perspective
(Elsevier, 2022) Jarad, Fahd; Riaz, Muhammad Bilal; Atangana, Abdon; Jarad, Fahd; Awrejcewicz, Jan; Matematik
In this article, a new approach to study the fractionalized Maxwell fluid is described by the Prabhakar fractional derivative near an exponentially accelerated vertical plate together with exponentially variable velocity, energy and mass diffusion through a porous media is critically examined. The phenomena has been described in forms of partial differential equations along with heat and mass transportation effect taken into account. The Prabhakar fractional operator which was recently introduced is used in this work together with generalized Fick's and Fourier's law. The fractionalized model is transfromed into non-dimensional form by using some suitable dimensionless quantities. The non-dimensional developed fractional model for momentum, thermal and diffusion equations based on Prabhakar fractional operator has been solved analytically via Laplace transformation method and calculated solutions expressed in terms of Mittag-Leffler special functions. Graphical demonstration are made to characterized the physical behavior of different parameters and significance of such system parameters over the momentum, concentration and energy profiles. Moreover, for results validation, comparative study among limiting models derived from fractionalized Prabhakar Maxwell fluid such as fractional and classical fluid models for Maxwell and Newtonian are performed. Further, it is observed from the graphs the valocity curves for classical fluid models relatively higher as compared to fractional fluid models, and fractional approach is more realistic and convenient as compared to classical approach.