Fen - Edebiyat Fakültesi

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Citation - WoS: 79
Citation - Scopus: 82
The (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation: Its Solitons and Jacobi Elliptic Function Solutions
(Springer Heidelberg, 2021) Salahshour, Soheil; Mirzazadeh, Mohammad; Ahmadian, Ali; Baleanu, Dumitru; Khoshrang, Arian; Hosseini, Kamyar; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The search for exact solutions of nonlinear evolution models with different wave structures has achieved significant attention in recent decades. The present paper studies a nonlinear (2+1)-dimensional evolution model describing the propagation of nonlinear waves in Heisenberg ferromagnetic spin chain system. The intended aim is carried out by considering a specific transformation and adopting a modified version of the Jacobi elliptic expansion method. As a result, a number of solitons and Jacobi elliptic function solutions to the Heisenberg ferromagnetic spin chain equation are formally derived. Several three-dimensional plots are presented to demonstrate the dynamical features of the bright and dark soliton solutions.
A 6-Point Subdivision Scheme and Its Applications for the Solution of 2nd Order Nonlinear Singularly Perturbed Boundary Value Problems
(Amer inst Mathematical Sciences-aims, 2020) Baleanu, Dumitru; Ejaz, Syeda Tehmina; Anju, Kaweeta; Ahmadian, Ali; Salahshour, Soheil; Ferrara, Massimiliano; Mustafa, Ghulam; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we first present a 6-point binary interpolating subdivision scheme (BISS) which produces a C-2 continuous curve and 4th order of approximation. Then as an application of the scheme, we develop an iterative algorithm for the solution of 2nd order nonlinear singularly perturbed boundary value problems (NSPBVP). The convergence of an iterative algorithm has also been presented. The 2nd order NSPBVP arising from combustion, chemical reactor theory, nuclear engineering, control theory, elasticity, and fluid mechanics can be solved by an iterative algorithm with 4th order of approximation.
Citation - WoS: 30
Citation - Scopus: 33
Abundant New Solutions of the Transmission of Nerve Impulses of an Excitable System
(Springer Heidelberg, 2020) Attia, Raghda A. M.; Baleanu, Dumitru; Khater, Mostafa M. A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This research investigates the dynamical behavior of the transmission of nerve impulses of a nervous system (the neuron) by studying the computational solutions of the FitzHugh-Nagumo equation that is used as a model of the transmission of nerve impulses. For achieving our goal, we employ two recent computational schemes (the extended simplest equation method and Sinh-Cosh expansion method) to evaluate some novel computational solutions of these models. Moreover, we study the stability property of the obtained solutions to show the applicability of them in life. For more explanation of this transmission, some sketches are given for the analytical obtained solutions. A comparison between our results and that obtained in previous work is also represented and discussed in detail to show the novelty for our solutions. The performance of the two used methods shows power, practical and their ability to apply to other nonlinear partial differential equations.
Citation - WoS: 22
Citation - Scopus: 22
Abundant Optical Solitons To the (2+1)-Dimensional Kundu-Mukherjee Equation in Fiber Communication Systems
(Springer, 2023) Baleanu, Dumitru; Ghanbari, Behzad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The Kundu-Mukherjee-Naskar equation holds significant relevance as a nonlinear model for investigating intricate wave phenomena in fluid and optical systems. This study uncovers new optical soliton solutions for the KMN equation by employing analytical techniques that utilize combined elliptic Jacobian functions. The solutions exhibit mixtures of distinct Jacobian elliptic functions, offering novel insights not explored in prior KMN equation research. Visual representations in the form of 2D ContourPlots elucidate the physical behaviors and properties of these newly discovered solution forms. The utilization of symbolic computations facilitated the analytical derivation of these solutions, offering a deeper understanding of the nonlinear wave dynamics governed by the KMN equation. These employed techniques showcase the potential for future analytical advancements in unraveling the complex soliton landscape of the multifaceted KMN model. The findings provide valuable insights into the intricacies of soliton behavior within this nonlinear system, offering new perspectives for analysis and exploration in areas such as fiber optic communications, ocean waves, and fluid mechanics. Maple symbolic packages have enabled us to derive analytical results.
Citation - WoS: 14
Citation - Scopus: 16
An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations
(Wiley-hindawi, 2017) Salahshour, S.; Ahmadian, A.; Ismail, F.; Baleanu, D.; Bishehniasar, M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs) to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs). The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE). Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD) method and standard finite difference (SFD) technique, which are popular in the literature for solving engineering problems.
Citation - WoS: 34
Adaptive Fractional-Order Blood Glucose Regulator Based on High-Order Sliding Mode Observer
(inst Engineering Technology-iet, 2019) Heydarinejad, Hamid; Baleanu, Dumitru; Delavari, Hadi; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Type I diabetes is described by the destruction of the insulin-producing beta-cells in the pancreas. Hence, exogenous insulin administration is necessary for Type I diabetes patients. In this study, to estimate the states that are not directly available from the Bergman minimal model a high-order sliding mode observer is proposed. Then fractional calculus is combined with sliding mode control (SMC) for blood glucose regulation to create more robustness performance and make more degree of freedom and flexibility for the proposed method. Then an adaptive fractional-order SMC is proposed. The adaptive SMC protect controller against disturbance and uncertainties while the fractional calculus provides robust performance. Numerical simulation verifies that the proposed controllers have better performance in the presence of disturbance and uncertainties without chattering.
Citation - WoS: 24
Citation - Scopus: 30
Advanced Exact Solutions To the Nano-Ionic Currents Equation Through Mts and the Soliton Equation Containing the Rlc Transmission Line
(Springer Heidelberg, 2023) Miah, M. Mamun; Iqbal, M. Ashik; Alshehri, Hashim M.; Baleanu, Dumitru; Osman, M. S.; Chowdhury, M. Akher; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this study, the double (G '/G, 1/G)-expansion method is utilized for illustrating the improved explicit integral solutions for the two of nonlinear evolution equations. To expose the importance and convenience of our assumed method, we herein presume two models, namely the nano-ionic currents equation and the soliton equation. The exact solutions are generated with the aid of our proposed method in such a manner that the solutions involve to the rational, trigonometric, and hyperbolic functions for the first presumed nonlinear equation as well as the trigonometric and hyperbolic functions for the second one with meaningful symbols that promote some unique periodic and solitary solutions. The method used here is an extension of the (G '/G)-expansion method to rediscover all known solutions. We offer 2D and 3D charts of the various recovery solutions to better highlight our findings. Finally, we compared our results with those of earlier solutions.
Citation - WoS: 28
Citation - Scopus: 28
Advanced Fractional Calculus, Differential Equations and Neural Networks: Analysis, Modeling and Numerical Computations
(Iop Publishing Ltd, 2023) Karaca, Yeliz; Vazquez, Luis; Macias-Diaz, Jorge E.; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Most physical systems in nature display inherently nonlinear and dynamical properties; hence, it would be difficult for nonlinear equations to be solved merely by analytical methods, which has given rise to the emerging of engrossing phenomena such as bifurcation and chaos. Conjointly, due to nonlinear systems' exhibiting more exotic behavior than harmonic distortion, it becomes compelling to test, classify and interpret the results in an accurate way. For this reason, avoiding preconceived ideas of the way the system is likely to respond is of pivotal importance since this facet would have effect on the type of testing run and processing techniques used in nonlinear systems. Paradigms of nonlinear science may suggest that it is 'the study of every single phenomenon' due to its interdisciplinary nature, which is another challenge encountered and needs to be addressed by generating and designing a systematic mathematical framework where the complexity of natural phenomena hints the requirement of identifying their commonalties and classifying their various manifestations in different nonlinear systems. Studying such common properties, concepts or paradigms can enable one to gain insight into nonlinear problems, their essence and consequences in a broad range of disciplines all forthwith. Fractional differential equations associated with non-local phenomena in physics have arisen as a powerful mathematical tool within a multidisciplinary research framework. Fractional differential equations, as one extension of the fractional calculus theory, can yield the evolution of various systems properly, which reinforces its position in mathematics and science while setting stage for the description of dynamic, complicated and nonlinear events. Through the reflection of the systems' actual properties, fractional calculus manifests unforeseeable and hidden variations, and thus, enables integration and differentiation, with the solutions to be approximated by numerical methods along with modeling and predicting the dynamics of multiphysics, multiscale and physical systems. Neural Networks (NNs), consisting of hidden layers with nonlinear functions that have vector inputs and outputs, are also considerably employed owing to their versatile and efficient characteristics in classification problems as well as their sophisticated neural network architectures, which make them capable of tackling complicated governing partial differential equation problems. Furthermore, partial differential equations are used to provide comprehensive and accurate models for many scientific phenomena owing to the advancements of data gathering and machine learning techniques which have raised opportunities for data-driven identification of governing equations derived from experimentally observed data. Given these considerations, while many problems are solvable and have been solved, efforts are still needed to be able to respond to the remaining open questions in the fields that have a broad range of spectrum ranging from mathematics, physics, biology, virology, epidemiology, chemistry, engineering, social sciences to applied sciences. With a view of different aspects of such questions, our special issue provides a collection of recent research focusing on the advances in the foundational theory, methodology and topical applications of fractals, fractional calculus, fractional differential equations, differential equations (PDEs, ODEs, to name some), delay differential equations (DDEs), chaos, bifurcation, stability, sensitivity, machine learning, quantum machine learning, and so forth in order to expound on advanced fractional calculus, differential equations and neural networks with detailed analyses, models, simulations, data-driven approaches as well as numerical computations.
Citation - WoS: 10
Citation - Scopus: 10
Aggregation Operators for Interval-Valued Pythagorean Fuzzy Hypersoft Set With Their Application To Solve Mcdm Problem
(Tech Science Press, 2023) Siddique, Imran; Ali, Rifaqat; Jarad, Fahd; Iampan, Aiyared; Zulqarnain, Rana Muhammad; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Experts use Pythagorean fuzzy hypersoft sets (PFHSS) in their investigations to resolve the indeterminate and imprecise information in the decision-making process. Aggregation operators (AOs) perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception. In this paper, we extend the concept of PFHSS to interval-valued PFHSS (IVPFHSS), which is the generalized form of interval -valued intuitionistic fuzzy soft set. The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set. It is the most potent method for amplifying fuzzy data in the decision-making (DM) practice. Some operational laws for IVPFHSS have been proposed. Based on offered operational laws, two inventive AOs have been established: interval-valued Pythagorean fuzzy hypersoft weighted average (IVPFHSWA) and interval-valued Pythagorean fuzzy hypersoft weighted geometric (IVPFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) shows an active part in contracts with the difficulties in industrial enterprise for material selection. But, the prevalent MCGDM approaches consistently carry irreconcilable consequences. Based on the anticipated AOs, a robust MCGDM technique is deliberate for material selection in industrial enterprises to accommodate this shortcoming. A real-world application of the projected MCGDM method for material selection (MS) of cryogenic storing vessels is presented. The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS.
Ample Spectrum Contractions in Branciari Distance Spaces
(Yokohama Publ, 2021) Karapinar, Erdal; Karapınar, Erdal; Lopez de Hierro, Antonio Francisco Roldan; Shahzad, Naseer; 19184; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Very recently, the notion of ample spectrum contraction has been introduced in order to unify, under the same axioms, a large number of contractive mappings that have had great success in the field of Fixed Point Theory in recent years and that have been used in a wide variety of applications in Nonlinear Analysis (Meir-Keeler contractions, Geragthy contractions, contractions under simulation functions, contractions under R-functions, etc.) However, the subtle conditions that define ample spectrum contractions cannot be extended as they are to new kinds of abstract metric spaces because they involve key properties that are only fulfilled in metric spaces. In this paper, based on a very recent work in which the authors unravel the essential properties of the topology in Branciari spaces, we investigate the reasons why the proposed axiomatic fails in Branciari spaces and we illustrate how to overcome such drawbacks. As a consequence, we characterize the notion of ample spectrum contraction in the setting of Branciari distance spaces and we also investigate the existence and uniqueness of fixed points for such family of contractions in the context of complete Branciari distance spaces.
Citation - WoS: 14
Citation - Scopus: 16
Analysis and Application Using Quad Compound Combination Anti-Synchronization on Novel Fractional-Order Chaotic System
(Springer Heidelberg, 2021) Trikha, Pushali; Baleanu, Dumitru; Jahanzaib, Lone Seth; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript, a novel fractional-order chaotic model has been investigated. The characteristic dynamics of the model have been investigated using various tools such as Lyapunov dynamics, bifurcation diagrams, equilibrium point analysis, Kaplan York dimension, existence and uniqueness of solution. The Lyapunov spectrum, bifurcation diagrams and attractors are discussed over a range of fractional order of 0.8 to 1. The considered system is synchronized by using a novel technique quad compound combination anti-synchronization using two control methods, viz. nonlinear and adaptive sliding mode technique. The obtained results of synchronization are compared with some existing literature and also illustrated its application in secure communication.
Citation - WoS: 3
Citation - Scopus: 2
Analysis and Numerical Effects of Time-Delayed Rabies Epidemic Model With Diffusion
(Walter de Gruyter Gmbh, 2023) Rehman, Muhammad Aziz-Ur; Ahmed, Nauman; Baleanu, Dumitru; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Raza, Ali; Jawaz, Muhammad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The current work is devoted to investigating the disease dynamics and numerical modeling for the delay diffusion infectious rabies model. To this end, a non-linear diffusive rabies model with delay count is considered. Parameters involved in the model are also described. Equilibrium points of the model are determined and their role in studying the disease dynamics is identified. The basic reproduction number is also studied. Before going towards the numerical technique, the definite existence of the solution is ensured with the help of the Schauder fixed point theorem. A standard result for the uniqueness of the solution is also established. Mapping properties and relative compactness of the operator are studied. The proposed finite difference method is introduced by applying the rules defined by R.E. Mickens. Stability analysis of the proposed method is done by implementing the Von-Neumann method. Taylor's expansion approach is enforced to examine the consistency of the said method. All the important facts of the proposed numerical device are investigated by presenting the appropriate numerical test example and computer simulations. The effect of tau on infected individuals is also examined, graphically. Moreover, a fruitful conclusion of the study is submitted.
Citation - WoS: 18
Citation - Scopus: 24
Analysis for Fractional-Order Predator-Prey Model With Uncertainty
(inst Engineering Technology-iet, 2019) Baleanu, Dumitru; Thangapandi, Kalidas; Perera, Shyam Sanjeewa Nishantha; Narayanamoorthy, Samayan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Here, the authors analyse the fractional-order predator-prey model with uncertainty, due to the vast applications in various ecological systems. The most of the ecological model do not have exact analytic solution, so they proposed a numerical technique for an approximate solution. In the proposed method, they have implemented the higher order term into the fractional Euler method to enhance the precise solution. Further, the present attempt is aimed to discuss the solutions of the FPPM with uncertainty (fuzzy) initial conditions. The initial conditions of the predator-prey model were taken as fuzzy initial conditions due to the fact that the ecological model highly depends on uncertain parameters such as growth/decay rate, climatic conditions, and chemical reactions. Finally, the numerical example manifest that the proposed method is authentic, applicable, easy to use from a computational viewpoint and the acquired outcomes are balanced with the existing method (HPM), which shows the efficiency of the proposed method.
Citation - WoS: 99
Citation - Scopus: 116
Analysis of a Fractional Model of the Ambartsumian Equation
(Springer Heidelberg, 2018) Singh, Jagdev; Baleanu, Dumitru; Rathore, Sushila; Kumar, Devendra; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The prime target of this work is to investigate a fractional model of the Ambartsumian equation. This equation is very useful to describe the surface brightness of the Milky Way. The Ambartsumian equation of fractional order is solved with the aid of the HATM. The solution is presented in terms of the power series, which is convergent for all real values of variables and parameters. The outcomes drawn with the help of the HATM are presented in the form of graphs.
Citation - WoS: 29
Citation - Scopus: 33
Analysis of Eyring-Powell Fluid Flow Used as a Coating Material for Wire With Variable Viscosity Effect Along With Thermal Radiation and Joule Heating
(Mdpi, 2020) Rasheed, Haroon Ur; Abbas, Tariq; Khan, Waris; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Zeeshan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This article examines a wire coating technique that considers how viscoelastic Eyring-Powell fluid is studied with magnetohydrodynamic (MHD) flow, thermal transfer, and Joule heating effects. Temperature-dependent variable and flexible viscosity models are considered. The interface boundary layer equalities which describe flux and thermal convective phenomena are evaluated using a dominant numerical technique-the so-called Runge-Kutta 4th-order method. A permeable matrix which behaves like a dielectric to avoid heat dissipation is taken into account and is the distinguishing aspect of this article. The effect of thermal generation is also explained, as it controls power. The effects of various parameters, such as non-Newtonian fluid, magnetic field, permeability, and heat source/sink, on wire coating processes are investigated through graphs and explained in detail. For the sake of validity, numerical techniques are compared with a semi-numerical technique (HAM) and BVPh2, and an outstanding agreement is found.
Citation - WoS: 23
Citation - Scopus: 27
Analysis of Mixed Type Nonlinear Volterra-Fredholm Integral Equations Involving the Erdelyi-Kober Fractional Operator
(Elsevier, 2023) Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; Paul, Supriya Kumar; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper investigates the existence, uniqueness and stability of solutions to the nonlinear Volterra-Fredholm integral equations (NVFIE) involving the Erdelyi-Kober (E-K) fractional integral operator. We use the Leray- Schauder alternative and Banach's fixed point theorem to examine the existence and uniqueness of solutions, and we also explore Hyers-Ulam (H-U) and Hyers-Ulam-Rassias (H-U-R) stability in the space C([0, fl], R). Furthermore, three solution sets U-sigma,U-lambda, U-theta,U-1 and U-1,U-1 are constructed for sigma > 0, lambda > 0, and theta is an element of (0,1), and then we obtain local stability of the solutions with some ideal conditions and by using Schauder fixed point theorem on these three sets, respectively. Also, to achieve the goal, we choose the parameters for the NVFIE as delta is an element of (1/2, 1), p is an element of (0,1), gamma > 0. Three examples are provided to clarify the results.
Citation - WoS: 2
Citation - Scopus: 3
Analysis of Mixed-Order Caputo Fractional System With Nonlocal Integral Boundary Condition
(Tubitak Scientific & Technological Research Council Turkey, 2018) Khodabakhshi, Neda; Baleanu, Dumitru; Akman Yildiz, Tugba; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper deals with a mixed-order Caputo fractional system with nonlocal integral boundary conditions. This study can be considered as an extension of previous studies, since the orders of the equations lie on different intervals. We discuss the existence and uniqueness of the solution using fixed point methods. We enrich the study with an example.
Citation - WoS: 4
Citation - Scopus: 5
Analysis of Multiple Slip Effects on Mhd Blood Peristaltic Flow of Phan-Thien Nanofluid Through an Asymmetric Channel
(World Scientific Publ Co Pte Ltd, 2023) Baleanu, Dumitru; Vaidya, Hanumesh; Prasad, K. V.; Khan, M. Ijaz; Bafakeeh, Omar T.; Galal, Ahmed M.; Choudhari, Rajashekhar; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The primary focus of this paper is to model the MHD peristaltic flow of Phan-Thien-Tanner nanofluid in an asymmetric channel while taking into account multiple slip effects. Approximations based on a long wavelength and a low Reynolds number are used to transform the governing partial differential equations into nonlinear and coupled differential equations. It is possible to obtain an exact solution to the problem of the distribution of temperature and the distribution of nanoparticle concentration. The perturbation technique is employed to solve the nonlinear velocity distribution. The graphical analysis illustrates the effects that essential and relevant parameters have on the velocity field, temperature distribution, nanoparticle concentration, skin friction coefficient, Nusselt number, Sherwood number, pressure rise, and trapping phenomena. The results that were obtained are essential to comprehending the rheology of blood.
Citation - WoS: 9
Citation - Scopus: 10
Analysis of the Effect of Potential Cycles on the Reflective Infrared Signals of Nitro Groups in Nanofilms: Application of the Fractional Moments Statistics
(Wiley-v C H verlag Gmbh, 2010) Alekhin, Alexander P.; Baleanu, Dumitru; Dinc, Erdal; Ustundag, Zafer; Eksi, Haslet; Solak, Ali Osman; Nigmatulin, Raoul R.; 6981; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The effect of the potential cycles on the reflective IR signals of nitro-groups in nanofilms was studied for the statistical characterization of nitrobenzene (NB) and nitroazobenzene (NAB)-modified glassy carbon (GC) surfaces. Both NB and NAB nanofilms were obtained by the electrochemical reduction of the diazonium tetrafluoroborate salts in acetonitrile using cyclic voltammetry (CV). The modified surfaces were denoted as GC-(NB)(n) and GC-(NAB)(n), respectively, where n indicates the number of CV cycles performed during modification. Reflective IR signals of the normalized NB and NAB nanofilms and GC were used for the quantitative evaluation of the effect of the potential cycles on the reflective IR signals of nitro-groups in nanofilms. The detection and quantitative 'reading' of the influence of number of CV cycles were realized in the frame of a new error controllable approach that was applied for analysis of all available set of data. This approach includes in itself the following basic steps: (a) the procedure of the division (normalization) on the GC spectra, (b) the comparison of the smoothed spectra for their statistical proximity in the frame of the statistics of the fractional moments, (c) extraction of possible calibration parameters for possible calibration of the normalized spectra with respect to the number of CV cycles. These three basic steps are becoming effective for detection of the influence of some external factors. In our case it is important to detect the influence of the factor n characterizing CV cycles.
Citation - WoS: 7
Citation - Scopus: 7
Analytical Approximate Solutions of (n+1)-Dimensional Fractal Heat-Like and Wave-Like Equations
(Mdpi, 2017) Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet Giyas; Acan, Omer; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.

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