Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 4Citation - Scopus: 6Existence and Ulam-Hyers Stability of Mild Solutions for Impulsive Integro-Differential Systems Via Resolvent Operators(Amer inst Mathematical Sciences-aims, 2025) Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, Erdal; Bensalem, AbdelhamidThe aim of this paper is to present existence, Ulam-Hyers-Rassias stability and continuous dependence on initial conditions for the mild solution of impulsive integro-differential systems via resolvent operators. Our analysis is based on fixed point theorem with generalized measures of noncompactness, this approach is combined with the technique that uses convergence to zero matrices in generalized Banach spaces. An example is presented to illustrate the efficiency of the result obtained.Article Citation - WoS: 5Citation - Scopus: 7A Fractional Study of Mhd Casson Fluid Motion With Thermal Radiative Flux and Heat Injection/Suction Mechanism Under Ramped Wall Condition: Application of Rabotnov Exponential Kernel(Sciendo, 2024) Jarad, Fahd; Riaz, Muhammad Bilal; Rehman, Aziz UrThe primary objective of this research is to extend the concept of fractionalized Casson fluid flow. In this study, a comprehensive analysis of magnetohydrodynamic (MHD) natural convective flow of Casson fluid is conducted, focusing on obtaining analytical solutions using the non-integer-order derivative known as the Yang-Abdel-Aty-Cattani (YAC) operator. The YAC operator utilized in this research possesses a more generalized exponential kernel. The fluid flow is examined in the vicinity of an infinitely vertical plate with a characteristic velocity denoted as u(0). The mathematical modelling of the problem incorporates partial differential equations, incorporating Newtonian heating and ramped conditions. To facilitate the analysis, a suitable set of variables is introduced to transform the governing equations into a dimensionless form. The Laplace transform (LT) is then applied to the fractional system of equations, and the obtained results are presented in series form and also expressed in terms of special functions. The study further investigates the influence of relevant parameters, such as alpha, beta, P-r, Q, Gr, M, N-r and K, on the fluid flow to reveal interesting findings. A comparison of different approaches reveals that the YAC method yields superior results compared to existing operators found in the literature. Graphs are generated to illustrate the outcomes effectively. Additionally, the research explores the limiting cases of the Casson and viscous fluid models to derive the classical form from the YAC fractionalized Casson fluid model.Article Citation - WoS: 10Citation - Scopus: 12Soliton Solutions for Non-Linear Kudryashov's Equation Via Three Integrating Schemes(Vinca inst Nuclear Sci, 2021) Mirhosseini-Alizamini, Mehdi; Baleanu, Dumitru; Rezazadeh, Hadi; Inc, Mustafa; Hussain, Majid; Arshed, Saima; Mirhosseini-Alizamini, Seyed Mehdi; Mustafa, I.N.C.This paper considers the non-linear Kudryashov's equation, that is an extension of the well-known dual-power law of refractive index and is analog to the generalized version of anti-cubic non-linearity. The model is considered in the presence of full non-linearity. The main objective of this paper is to extract soliton solutions of the proposed model. Three state-of-the-art integration schemes, namely modified auxiliary equation method, the sine-Gordon expansion method and the tanh-coth expansion method have been employed for obtaining the desired soliton solutions.Article Citation - WoS: 38Citation - Scopus: 31Prabhakar Fractional Derivative and Its Applications in the Transport Phenomena Containing Nanoparticles(Vinca inst Nuclear Sci, 2021) Zahid, Muhammad; Chu, Yu-Ming; Baleanu, Dumitru; Asjad, Muhammad ImranIn this paper, a new approach of analytical solutions is carried out on the thermal transport phenomena of Brinkman fluid based on Prabhakar's fractional derivative with generalized Fourier's law. The governing equations are obtained through constitutive relations and analytical solutions obtained via Laplace transform technique. Solutions for temperature and velocity field were analyzed through graphical description by MathCad software. The fluid properties revealed various aspects for different flow parameters as well as fractional parameter values and found important results. As a result, it is found that fluid properties can be enhanced by increasing the values of fractional parameters and can be useful in some experimental data where suitable.Article Citation - WoS: 1Citation - Scopus: 1Studying Heat Conduction in a Sphere Considering Hybrid Fractional Derivative Operator(Vinca inst Nuclear Sci, 2022) Latif, Mohamed S. Abdel; Baleanu, Dumitru; Kader, Abass H. AbdelIn this paper, the fractional heat equation in a sphere with hybrid fractional derivative operator is investigated. The heat conduction is considered in the case of central symmetry with heat absorption. The closed form solution in the form of three parameter Mittag-Leffler function is obtained for two Dirichlet boundary value problems. The joint finite sine Fourier-Laplace transform is used for solving these two problems. The dynamics of the heat transfer in the sphere is illustrated through some numerical examples and figures.Article Citation - WoS: 2Citation - Scopus: 2Study of Electro-Osmotic Nanofluid Transport for Scraped Surface Heat Exchanger With Heat Transfer Phenomenon(Vinca inst Nuclear Sci, 2021) Imran, Ali; Javeed, Shumaila; Baleanu, Dumitru; Zeb, Muhammad; Ahmad, Sohail; Waheed, AsifIn this study a novel mathematical model for electroosmotic flow for Cu-water based nanofluid with heat transfer phenomenon is reported for scraped-surface heat exchanger. The flow is initiated due to motion of lower wall of the channel and axial pressure gradient. The flow is modelled with aid of low Reynolds number and lubrication approximation theory. Exact analytical expressions are gathered for axial velocity, and stream functions for various stations of scraped-surface heat exchanger. Physical phenomenon of electro osmotic parameter are investigated on velocity profile, velocity distribution and pressure rise at edge of the blades. It is reported that electro-osmotic parameter mainly works as dragging force, it can be used to control the flow. This controlling mechanism may be helpful in mixing different materials in scraped-surface heat exchanger. Pressure rise at edge of the blades mainly rises below the blades with electro-osmotic, whereas, this profiles is suppressed for region above the blades and between the blades.Conference Object Citation - WoS: 1Strengthening of Columns With Different Innovative Composite Materials for Rc Buildings Without Sufficient Earthquake Resistance(Gazi Univ, 2022) Mercimek, Omer; Ghoroubi, Rahim; Ozdemir, Anil; Anil, OzgurThe Turkey includes the world's second most active faults and is geographically situated at a very high seismic activity. Research on strengthening RC (reinforced-concrete) structures without adequate earthquake resistance has become an extremely important issue. Taking into account the objectives of this research, an experimental study is designed to strengthen the columns without adequate earthquake resistance by using carbon-reinforced-fiber-fabric (CFRP) strips and textile-reinforced-mortar (TRM) layers with two separate types of advanced composite materials. The variables evaluated within the study horizon are the composite material type used for strengthening, the width of the strip, and whether or not the anchor is used at the point of strip overlap. In this experiment, nine RC column were produced and were tested by affecting axial load, which are the reference test specimens without strengthening and eight RC column test specimens strengthened with two separate types of composite material. The loaddisplacement behavior, initial stiffness value, energy dissipation capacities, ultimate load capacity and displacement ductility ratios have been measured according to the test results. It was also examined which of the two different composite materials used to strengthen the columns of the RC is more efficient in improving the columns performance.Article Citation - WoS: 9Citation - Scopus: 11Fractional Model of Second Grade Fluid Induced by Generalized Thermal and Molecular Fluxes With Constant Proportional Caputo(Vinca inst Nuclear Sci, 2021) Ahmad, Mushtaq; Asjad, Muhammad Imran; Baleanu, Dumitru; Chu, Yu-MingIn this research article, the constant proportional Caputo approach of fractional derivative is applied to derive the generalized thermal and molecular profiles for flow of second grade fluid over a vertical plate. The governing equations of the prescribed flow model are reduced to dimensionless form and then solved for temperature, concentration, and velocity via Laplace transform. Further graphs of field variables are sketched for parameter of interest. Comparison between present result and the existing results is also presented graphically.Article Citation - WoS: 1Citation - Scopus: 1Fractional Heat Equation Optimized by a Chaotic Function(Vinca inst Nuclear Sci, 2021) Wazi, Mayada T.; Baleanu, Dumitru; Al-Saidi, Nadia; Ibrahim, Rabha W.In this effort, we propose a new fractional differential operator in the open unit disk. The operator is an extension of the Atangana-Baleanu differential operator without singular kernel. We suggest it for a normalized class of analytic functions in the open unit disk. By employing the extended operator, we study the time-2-D space heat equation and optimizing its solution by a chaotic function.Article Citation - WoS: 14Citation - Scopus: 13Exact Solutions of Stochastic Kdv Equation With Conformable Derivatives in White Noise Environment(Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Ulutas, EsmaIn this article, we have considered Wick-type stochastic Korteweg de Vries (KdV) equation with conformable derivatives. By the help of white noise analysis, Hermit transform and extended G/G-expansion method, we have obtained exact travelling wave solutions of KdV equation with conformable derivatives. We have applied the inverse Hermit transform for stochastic soliton solutions and then we have shown how stochastic solutions can be presented as Brownian motion functional solutions by an application example.