Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Citation - WoS: 9
Citation - Scopus: 12
The Caputo-Fabrizio Time-Fractional Sharma-Tasso Equation and Its Valid Approximations
(Iop Publishing Ltd, 2022) Ilie, Mousa; Mirzazadeh, Mohammad; Baleanu, Dumitru; Park, Choonkil; Salahshour, Soheil; Hosseini, Kamyar
Studying the dynamics of solitons in nonlinear time-fractional partial differential equations has received substantial attention, in the last decades. The main aim of the current investigation is to consider the time-fractional Sharma-Tasso-Olver-Burgers (STOB) equation in the Caputo-Fabrizio (CF) context and obtain its valid approximations through adopting a mixed approach composed of the homotopy analysis method (HAM) and the Laplace transform. The existence and uniqueness of the solution of the time-fractional STOB equation in the CF context are investigated by demonstrating the Lipschitz condition for phi(x, t; u) as the kernel and giving some theorems. To illustrate the CF operator effect on the dynamics of the obtained solitons, several two- and three-dimensional plots are formally considered. It is shown that the mixed approach is capable of producing valid approximations to the time-fractional STOB equation in the CF context.
Citation - WoS: 9
Citation - Scopus: 21
Study of Implicit Type Coupled System of Non-Integer Order Differential Equations With Antiperiodic Boundary Conditions
(Wiley, 2019) Shah, Kamal; Khan, Rahmat Ali; Baleanu, Dumitru; Samina
In this paper, the first purpose is to study existence and uniqueness of solutions to a system of implicit fractional differential equations (IFDEs) equipped with antiperiodic boundary conditions (BCs). To obtain the mentioned results, we use Schauder's and Banach fixed point theorem. The second purpose is discussing the Ulam-Hyers (UH) and generalized Ulam-Hyers (GUH) stabilities for the respective solutions. An example is provided to illustrate the established results.
Citation - WoS: 7
Citation - Scopus: 9
The Investigation of Fe3o4 Atomic Aggregation in a Nanochannel in the Presence of Magnetic Field: Effects of Nanoparticles Distance Center of Mass, Temperature and Total Energy Via Molecular Dynamics Approach
(Elsevier, 2022) Fagiry, Moram A.; Sajadi, S. Mohammad; Almasri, Radwan A.; Karimipour, Arash; Li, Zhixiong; Ghaemi, Ferial; Liu, Xinglong
The computational procedure was utilized to explain the size effect of Fe3O4 nanoparticles on atomic behavior and phenomena of nanoparticles accumulation in nanochannel of ideal platinum (Pt) and the external magnetic field. Argon (Ar) atoms were considered as the base liquid, and the molecular dynamics procedure was utilized in this investigation. We utilized the Lennard-Jones potential to interact between the particles, whereas the nanochannel and nanoparticles structures were simulated. To compute the atomic manner, the quantities of nanoparticles distance center of mass, and the aggregation duration were presented. The outcomes implied that the nanoparticles size had a significant role in the accumulation. As the nanoparticles' size increased, the accumulation time of nanoparticles reached to 1.29 ns. Also, the outer magnetic field could severly postpone this event. (C) 2021 Published by Elsevier B.V.
Citation - WoS: 119
Citation - Scopus: 138
New Aspects of Fractional Biswas-Milovic Model With Mittag-Leffler Law
(Edp Sciences S A, 2019) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
This article deals with a fractional extension of Biswas-Milovic (BM) model having Kerr and parabolic law nonlinearities. The BM model plays a key role in describing the long-distance optical communications. The fractional homotopy analysis transform technique (FHATM) is applied to examine the BM equation involving Atangana-Baleanu (AB) derivative of fractional order. The FHATM is constructed by using homotopy analysis technique, Laplace transform algorithm and homotopy polynomials. The numerical simulation work is performed with the aid of maple software package. In order to demonstrate the effects of order of AB operator, variables and parameters on the displacement, the results are shown graphically. The outcomes of the present investigation are very encouraging and show that the AB fractional operator is very useful in mathematical modelling of natural phenomena.
Citation - WoS: 143
Citation - Scopus: 157
Semi-Analytical Study of Pine Wilt Disease Model With Convex Rate Under Caputo-Febrizio Fractional Order Derivative
(Pergamon-elsevier Science Ltd, 2020) Jarad, Fahd; Abdeljawad, Thabet; Shah, Kamal; Alqudah, Manar A.
In this paper, we present semi-analytical solution to Pine Wilt disease (PWD) model under the CaputoFabrizio fractional derivative (CFFD). For the proposed solution, we utilize Laplace transform coupled with Adomian decomposition method abbreviated as (LADM). The concerned method is a powerful tool to obtain semi-analytical solution for such type of nonlinear differential equations of fractional order (FODEs) involving non-singular kernel. Furthermore, we give some results for the existence of solution to the proposed model and present numerical results to verify the established analysis. (C) 2020 Elsevier Ltd. All rights reserved.
Citation - WoS: 26
Citation - Scopus: 32
On a More General Fractional Integration by Parts Formulae and Applications
(Elsevier, 2019) Gomez-Aguilar, J. F.; Jarad, Fahd; Abdeljawad, Thabet; Atangana, Abdon
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: 29
Citation - Scopus: 36
A Tau-Like Numerical Method for Solving Fractional Delay Integro-Differential Equations
(Elsevier, 2020) Ostadzad, M. H.; Baleanu, D.; Shahmorad, Sedaghat
In this paper, an operational matrix formulation of the Tau method is herein discussed to solve a class of delay fractional integrodifferential equations. The approximate solution is sought by using a suitable matrix representation of fractional and delay integrals. An error bound is herein for the first time discussed. Numerical examples show the effectiveness of the method. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
Citation - WoS: 178
Citation - Scopus: 189
On Fractional Calculus with General Analytic Kernels
(Elsevier Science Inc, 2019) Fernandez, Arran; Ozarslan, Mehmet Ali; Baleanu, Dumitru
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel functions. We demonstrate, under some assumptions, how all of these modifications can be considered as special cases of a single, unifying, model of fractional calculus. We provide a fundamental connection with classical fractional calculus by writing these general fractional operators in terms of the original Riemann-Liouville fractional integral operator. We also consider inversion properties of the new operators, prove analogues of the Leibniz and chain rules in this model of fractional calculus, and solve some fractional differential equations using the new operators. (C) 2019 Elsevier Inc. All rights reserved.
On Hardy-Hilbert Inequalities With Α-Fractional Derivatives
(Amer inst Mathematical Sciences-aims, 2023) Hassanein, Wael S.; Elsayed, Marwa Sh.; Baleanu, Dumitru; El-Deeb, Ahmed A.; Ahmed, Marwa M.
In the current manuscript, new alpha delta dynamic Hardy-Hilbert inequalities on time scales are discussed. These inequalities combine and expand a number of continuous inequalities and their corresponding discrete analogues in the literature. We shall illustrate our results using Holder's inequality on time scales and a few algebraic inequalities.
Citation - WoS: 23
Citation - Scopus: 26
New Newton's Type Estimates Pertaining To Local Fractional Integral Via Generalized P-Convexity With Applications
(World Scientific Publ Co Pte Ltd, 2021) Rashid, Saima; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-ming; LI, Yong-min
This paper aims to investigate the notion of p-convex functions on fractal sets Double-struck capital R-alpha(0 < alpha <= 1). Based on these novel ideas, we derived an auxiliary result depend on a three-step quadratic kernel by employing generalized p-convexity. Take into account the local fractal identity, we established novel Newton's type variants for the local differentiable functions. Several special cases are apprehended in the light of generalized convex functions and generalized harmonically convex functions. This novel strategy captures several existing results in the relative literature. Application is obtained in cumulative distribution function and generalized special weighted means to confirm the relevance and computational effectiveness of the considered method. Finally, we supposed that the consequences of this paper can stimulate those who are interested in fractal analysis.
Citation - WoS: 89
Citation - Scopus: 104
Hybrid Nanofluid on Mixed Convective Radiative Flow From an Irregular Variably Thick Moving Surface With Convex and Concave Effects
(Elsevier, 2020) Shafiq, Anum; Zaib, A.; Baleanu, Dumitru; Khan, Umair
The analysis explores the significance of thermal radiation on mixed convective boundary layer flow of a hybrid (SiO2-MoS2/H2O) nanofluid. The permeability of the stretched/shrinking surface is allowing the wall fluid suction, whereas radiation phenomenon is also incorporated in the presence of thermal convection. The combination of SiO2 nanoparticles and MoS2/H2O nanofluid are being modeled using the analytical nanofluid hybrid model in the present work. The hybrid nanofluid governing equations are transformed utilizing the similarity transformation technique. The transformed boundary value problem, then solved by bvp4c technique in MATLAB software. For specified values of various parameters the numerical results are obtained. The findings indicate dual solutions, up to some amount of stretching/shrinking parameter. The suction parameter decelerates the friction factor and accelerates the heat transfer rate. Also, the tem-perature augments due to the radiation and nanoparticles volume fraction in both solutions, whereas the velocity declines due to nanoparticles volume fraction.
Citation - WoS: 25
Citation - Scopus: 29
Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid With Newtonian Heating: Prabhakar Fractional Derivative Approach
(Mdpi, 2022) Jarad, Fahd; Riaz, Muhammad Bilal; Shah, Zaheer Hussain; Rehman, Aziz Ur
In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier's law and Fick's law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as alpha, Pr, beta, Sc, Gr, gamma, and Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.
Citation - WoS: 9
Citation - Scopus: 14
Finite Element Least Square Technique for Newtonian Fluid Flow Through a Semicircular Cylinder of Recirculating Region Via Comsol Multiphysics
(Hindawi Ltd, 2020) Memon, Abid A.; Memon, M. Asif; Bhatti, Kaleemullah; Shaikh, Gul M.; Baleanu, Dumitru; Alhussain, Ziyad A.; Khan, Ilyas
This article aims to study Newtonian fluid flow modeling and simulation through a rectangular channel embedded in a semicircular cylinder with the range of Reynolds number from 100 to 1500. The fluid is considered as laminar and Newtonian, and the problem is time independent. A numerical procedure of finite element's least Square technique is implemented through COMSOL multiphysics 5.4. The problem is validated through asymptotic solution governed through the screen boundary condition. The vortex length of the recirculating region formed at the back of the cylinder and orientation of velocity field and pressure will be discussed by three horizontal and four vertical lines along the recirculating region in terms of Reynolds number. It was found that the two vortices of unequal size have appeared and the lengths of these vortices are increased with the increase Reynolds number. Also, the empirical equations through the linear regression procedure were determined for those vortices. The orientation of the velocity magnitude as well as pressure along the lines passing through the center of upper and lower vortices are the same.
Citation - WoS: 37
Citation - Scopus: 41
New Solitary Wave Solutions and Stability Analysis of the Benney-Luke and the Phi-4 Equations in Mathematical Physics
(Amer inst Mathematical Sciences-aims, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Ghanbari, Behzad
In this paper, we present new solitary wave solutions for the Benney-Luke equation (BLE) and Phi-4 equation (PE). The new generalized rational function method (GERFM) is used to reach such solutions. Moreover, the stability for the governing equations is investigated via the aspect of linear stability analysis. It is proved that, both the governing equations are stable. We can also solve other nonlinear system of PDEs which are involve in mathematical physics and many other branches of physical sciences with the help of this new method.
Citation - WoS: 2
Citation - Scopus: 2
Hamiltonian Formulation of Singular Lagrangians on Time Scales
(Iop Publishing Ltd, 2008) Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet
The Hamiltonian formulation of Lagrangian on time scale is investigated and the equivalence of Hamilton and Euler-Lagrange equations is obtained. The role of Lagrange multipliers is discussed.
Citation - WoS: 12
Citation - Scopus: 12
A Kamenev-Type Oscillation Result for a Linear (1+α)-Order Fractional Differential Equation
(Elsevier Science inc, 2015) Mustafa, Octavian G.; O'Regan, Donal; Baleanu, Dumitru
We investigate the eventual sign changing for the solutions of the linear equation (x((alpha)))' + q(t)x = t >= 0, when the functional coefficient q satisfies the Kamenev-type restriction lim sup 1/t epsilon integral(t)(to) (t - s)epsilon q(s)ds = +infinity for some epsilon > 2; t(0) > 0. The operator x((alpha)) is the Caputo differential operator and alpha is an element of (0, 1). (C) 2015 Elsevier Inc. All rights reserved.
Citation - WoS: 8
Citation - Scopus: 11
A Study of Behaviour for Fractional Order Diabetes Model Via the Nonsingular Kernel
(Amer inst Mathematical Sciences-aims, 2022) Jaradz, Fahd; Jawa, Taghreed M.; Rashid, Sauna
A susceptible diabetes comorbidity model was used in the mathematical treatment to explain the predominance of mellitus. In the susceptible diabetes comorbidity model, diabetic patients were divided into three groups: susceptible diabetes, uncomplicated diabetics, and complicated diabetics. In this research, we investigate the susceptible diabetes comorbidity model and its intricacy via the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). The analysis backs up the idea that the aforesaid fractional order technique plays an important role in predicting whether or not a person will develop diabetes after a substantial immunological assault. Using the fixed point postulates, several theoretic outcomes of existence and Ulam's stability are proposed for the susceptible diabetes comorbidity model. Meanwhile, a mathematical approach is provided for determining the numerical solution of the developed framework employing the Adams type predictor-corrector algorithm for the ABC-fractional integral operator. Numerous mathematical representations correlating to multiple fractional orders are shown. It brings up the prospect of employing this structure to generate framework regulators for glucose metabolism in type 2 diabetes mellitus patients.
Citation - WoS: 88
Modeling and Simulation of the Fractional Space-Time Diffusion Equation
(Elsevier Science Bv, 2016) Miranda-Hernandez, M.; Lopez-Lopez, M. G.; Alvarado-Martinez, V. M.; Baleanu, D.; Gomez-Aguilar, J. F.
In this paper, the space-time fractional diffusion equation related to the electromagnetic transient phenomena in transmission lines is studied, three cases are presented; the diffusion equation with fractional spatial derivative, with fractional temporal derivative and the case with fractional space-time derivatives. For the study cases, the order of the spatial and temporal fractional derivatives are 0 < beta, gamma <= 2. respectively. In this alternative representation we introduce the appropriate fractional dimensional parameters which characterize consistently the existence of the fractional space-time derivatives into the fractional diffusion equation. The general solutions of the proposed equations are expressed in terms of the multivariate Mittag-Leffler functions; these functions depend only on the parameters beta and gamma and preserve the appropriated physical units for any value of the fractional derivative exponent. Furthermore, an analysis of the fractional time constant was made in order to indicate the change of the medium properties and the presence of dissipation mechanisms. The proposed mathematical representation can be useful to understand electrochemical phenomena, propagation of energy in dissipative systems, irreversible thermodynamics, quantum optics or turbulent diffusion, thermal stresses, models of porous electrodes, the description of gel solvents and anomalous complex processes. (C) 2015 Elsevier B.V. All rights reserved.
Citation - Scopus: 14
An Exploration of Heat and Mass Transfer for Mhd Flow of Brinkman Type Dusty Fluid Between Fluctuating Parallel Vertical Plates With Arbitrary Wall Shear Stress
(Elsevier B.V., 2024) Ali, G.; Kumam, P.; jarad, F.; khan, D.
An equitably complex phenomenon, the Brinkman-type dusty fluid and wall shear stress effect, is utilized in various engineering and product-making fields. For instance, dusty fluids are employed in nuclear-powered reactors and gas freezing systems to reduce heat of the system. To ascertain the impact of wall shear stress on Brinkman-type dusty fluid flow, the current study intends to do so. Base on this motivation, this paper discusses the two-phase MHD fluctuating flow of a Brinkman-type dusty fluid along with heat and mass transport. Two parallel non-conducting plates are used to model the flow, one at rest and the other in motion. Heat and mass transfer, along with wall share stress, are also taken into consideration, and plate fluctuation allows the flow to occur. The Poincaré-Lighthill fluctuation method was utilised in the process to investigate systematic solutions. The findings were achieved and plotted on a graph. The two-phase flow model is created by independently simulating the fluid and dust particle equations. The effect of relevant aspects such as the Grashof number, magnetic parameter, heat flux, and dusty fluid variable on the base fluid velocity has been explored. It was found that as the magnetic flux and imposed shear force decrease, the velocity of the base fluid increases. Additionally estimated in tabular form are rate of heat transfer and skin friction, two crucial fluid parameters for engineers. According to the graphical analysis, the Brinkman kind dusty fluid has better control over dust particle and fluid velocity rather than viscous fluid. By adjusting the value of N, you may control the temperature profile. Also, by adjusting the value of Sc and γ, you may control the concentration profile. © 2023 The Authors
Citation - WoS: 4
Special Issue Section on Fractal Ai-Based Analyses and Applications To Complex Systems: Part I
(World Scientific Publ Co Pte Ltd, 2021) Baleanu, Dumitru; Moonis, Majaz; Muhammad, Khan; Zhang, Yu-Dong; Gervasi, Osvaldo; Karaca, Yeliz

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