Matematik Bölümü

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About fractional calculus of singular Lagrangians
(IEEE, 2004) Baleanu, Dumitru
In this paper the solutions of the fractional Euler-Lagrange equations corresponding to singular fractional Lagrangians were examined. Despite of the complexity of solutions in the fractional case the gauge classical symmetry was preserved. Four examples of fractional singular Lagrangians were analyzed in details.
Citation - WoS: 3
Citation - Scopus: 6
Adomian-Pade Approximate Solutions To the Conformable Non-Linear Heat Transfer Equation
(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa
This paper adopts the Adomian decomposition method and the Pade approximation technique to derive the approximate solutions of a conformable heat transfer equation by considering the new definition of the Adomian polynomials. The Pade approximate solutions are derived along with interesting figures showing the approximate solutions.
Citation - WoS: 5
Citation - Scopus: 7
An Adoptive Renewable Energy Resource Selection Using Hesitant Pythagorean Fuzzy Dematel and Vikor Methods
(Ios Press, 2022) Narayanamoorthy, Samayan; Kang, Daekook; Baleanu, Dumitru; Geetha, Selvaraj
Nowadays, energy from renewable energy resources (RERs) partially satisfies society's energy demands. Investment in the renewable energy system is an arduous task because of huge investments. Generally, RERs selection involves conflicting criteria. Hence there is necessary to evaluate the RERs alternatives in economic, technological, and environmental aspects. Here, DEMATEL (Decision Making Trial and Evaluation Laboratory) method has been utilized to assess the interrelationship among the criteria under hesitant Pythagorean fuzzy (HPF) information. The Pythagorean fuzzy set (PFS) has recently obtained enormous attention and is applied widely in decision-making. We have proposed an integrating model with DEMATEL and VIKOR (Vise Kriterijumska Optimizacija Kompromisno Resenje) methods to identify and evaluate the criteria and alternatives in RERs selection. Within the proposed model, the HPF-DEMATEL method is utilized for weighting the criteria, and the HPF-VIKOR method is utilized for ranking. Finally, an illustrative example demonstrates the proposed method.
Advanced Modelling of Transport Problems in Heat-Mass and Related Fluid Mechanics
(Vinca inst Nuclear Sci, 2021) Hristov, Jordan; Baleanu, Dumitru; Kumar, Devendra; Baleanu, Dumitru; Matematik
Citation - WoS: 7
Analysis O a Caputo Hiv and Malaria Co-Infection Epidemic Model
(Chiang Mai Univ, Fac Science, 2021) Ahmed, Idris; Jarad, Fahd; Yusuf, Abdullahi; Sani, Musbahu Aminu; Jarad, Fahd; Kumam, Wiyada; Thounthong, Phatiphat; Matematik
In this paper, we investigate a fractional-order compartmental HIV and Malaria co-infection epidemic model using the Caputo derivative. The existence and uniqueness of the solution to the proposed fractional-order model were investigated using fixed point theorem techniques. To demonstrate that the proposed fractional-order model is both mathematically and epidemiologically well-posed, we compute the model's positivity and boundedness, which is an important feature in epidemiology. Finally, we analyze the dynamic behavior of each of the state variables using a recent and powerful computational technique known as the fractional Euler method.
Citation - WoS: 12
Citation - Scopus: 12
Analysis of Fractional Non-Linear Diffusion Behaviors Based on Adomian Polynomials
(Vinca inst Nuclear Sci, 2017) Baleanu, Dumitru; Luo, Wei-Hua; Wu, Guo-Cheng
A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.
Citation - WoS: 8
Analysis of Meningitis Model: a Case Study of Northern Nigeria
(Amer inst Mathematical Sciences-aims, 2020) Olamilekan, Lawal Ibrahim; Yusuf, Abdullahi; Baleanu, Dumitru; Baba, Isa Abdullahi
A new strain of meningitis emerges in northern Nigeria, which brought a lot of confusion. This is because vaccine and treatment for the old strain was adopted but to no avail. It was later discovered that it was a new strain that emerged. In this paper we consider the two strains of meningitis (I 1 and I 2). Our aim is to analyse the effect of one strain on the dynamics of the other strain mathematically. Equilibrium solutions were obtained and their global stability was analysed using Lyaponuv function. It was shown that the stability depends on magnitude of the basic reproduction ratio. The coexistence of the two strains was numerically shown.
Citation - WoS: 8
Citation - Scopus: 13
Analysis of Riccati Differential Equations Within a New Fractional Derivative Without Singular Kernel
(Ios Press, 2017) Lia, Atena; Tejadodi, Haleh; Baleanu, Dumitru; Jafari, Hossein
Recently Caputo and Fabrizio suggested new definition of fractional derivative that the new kernel has no singularity. In this paper, an analytical method for solving Riccati differential equation with a new fractional derivative is reported. We present numerical results of solving the fractional Riccati differential equations by using the variational iteration method and its modification. The obtained results of two methods demonstrate the efficiency and simplicity of the MVIM that gives good approximations for a larger interval.
Citation - WoS: 7
Citation - Scopus: 13
Analysis of the Impact of Thermal Radiation and Velocity Slip on the Melting of Magnetic Hydrodynamic Micropolar Fluid-Flow Over an Exponentially Stretching Sheet
(Vinca inst Nuclear Sci, 2023) Singh, Jagdev; Mehta, Ruchika; Kumar, Devendra; Baleanu, Dumitru; Kumar, Ravindra
The belongings of radiation and velocity slip on MHD stream and melting warmth transmission of a micropolar liquid over an exponentially stretched sheet which is fixed in a porous medium with heat source/sink are accessible. Homothety trans-forms the major PDE into a set of non-linear ODE. Then, by varying the boundary value problem to the initial value problem first, we get a numerical solution the non-linear system of equations. It has been observed that related parameters have a significant effect on flow and heat transfer characteristics, which are demonstrat-ed and explained in aspect done their figures. Velocity and temperature decrease by an extension in the magnetic aspect, and the angular velocity increase but the reverse effects come in melting, microrotation, and mixed convection parameters. The surface resistance coefficient as well as couple stress both decreases with amplification in the Eckert number microrotation, material, radiation, and heat source/sink parameter but the heat transport coefficient increase.
Citation - WoS: 2
Citation - Scopus: 2
Approximate Solutions and Conservation Laws of the Periodic Base Temperature of Convective Longitudinal Fins in Thermal Conductivity
(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa
In this paper, the residual power series method is used to study the numerical approximations of a model of oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. It is shown that the residual power series method is efficient for examining numerical behavior of non-linear models. Further, the conservation of heat is studied using the multiplier method.
Citation - WoS: 3
Citation - Scopus: 9
Artificial Intelligence Computing Analysis of Fractional Order Covid-19 Epidemic Model
(Aip Publishing, 2023) Baleanu, Dumitru; Cheema, Tahir Nawaz; Fadhal, Emad; Ibrahim, Rashid I. H.; Abdelli, Nouara; Raza, Ali
Artificial intelligence plays a very prominent role in many fields, and of late, this term has been gaining much more popularity due to recent advances in machine learning. Machine learning is a sphere of artificial intelligence where machines are responsible for doing daily chores and are believed to be more intelligent than humans. Furthermore, artificial intelligence is significant in behavioral, social, physical, and biological engineering, biomathematical sciences, and many more disciplines. Fractional-order modeling of a real-world problem is a powerful tool for understanding the dynamics of the problem. In this study, an investigation into a fractional-order epidemic model of the novel coronavirus (COVID-19) is presented using intelligent computing through Bayesian-regularization backpropagation networks (BRBFNs). The designed BRBFNs are exploited to predict the transmission dynamics of COVID-19 disease by taking the dataset from a fractional numerical method based on the Grunwald-Letnikov backward finite difference. The datasets for the fractional-order mathematical model of COVID-19 for Wuhan and Karachi metropolitan cities are trained with BRBFNs for biased and unbiased input and target values. The proposed technique (BRBFNs) is implemented to estimate the integer and fractional-order COVID-19 spread dynamics. Its reliability, effectiveness, and validation are verified through consistently achieved accuracy metrics that depend on error histograms, regression studies, and mean squared error.
Citation - WoS: 3
Citation - Scopus: 3
Automorphisms of Braid Groups on Closed Surfaces Which Are Not S², T², P² or the Klein Bottle
(World Scientific Publ Co Pte Ltd, 2006) Zhang, Ping
Consider a surface braid group of n strings as a subgroup of the isotopy group of homeomorphisms of the surface permuting n fixed distinguished points. Each automorphism of the surface braid group (respectively, of the special surface braid group) is shown to be a conjugate action on the braid group (respectively, on the special braid group) induced by a homeomorphism of the underlying surface if the closed surface, either orientable or non-orientable, is of negative Euler characteristic. In other words, the group of automorphisms of such a surface braid group is isomorphic to the extended mapping class group of the surface with n punctures, while the outer automorphism group of the surface braid group is isomorphic to the extended mapping class group of the closed surface itself.
Citation - WoS: 11
Citation - Scopus: 11
Best Proximity Results on Condensing Operators Via Measure of Noncompactness With Application To Integral Equations
(Chiang Mai Univ, Fac Science, 2020) Gabeleh, Moosa; Karapınar, Erdal; Asadi, Mehdi; Karapinar, Erdal; Matematik
We prove the best proximity point results for condensing operators on C-class of functions, by using a concept of measure of noncompactness. The results are applied to show the existence of a solution for certain integral equations. We express also an illsutrative examples to indicate the validity of the observed results.
Citation - WoS: 27
Citation - Scopus: 29
Boride Layer Growth Kinetics of Aisi H13 Steel Borided With Nano-Sized Powders
(Polska Akad Nauk, Polish Acad Sciences, inst Metall & Mater Sci Pas, 2018) Kanca, E.; Yilmaz, E.; Karakas, M. S.; Gunen, A.
Growth kinetics of boride layers in AISI H13 steel was investigated using the pack bonding method at temperatures of 1073, 1173 and 1273 K (800 degrees C, 900 degrees C and 1000 degrees C) for periods of 2, 4 and 6 h with nano-sized boron (NB) and micron-sized Ekabor II powders as bonding agents. The total thickness of the boride layer (including both FeB and Fe2B) after boriding at 1273 K (1000 degrees C) for 6 h was 103.8 gm and 96.5 mu m for the NB and Ekabor II specimens, respectively. X-ray diffraction analysis of the boride layers on the surfaces borided with NB and Ekabor II revealed the presence of FeB and Fe2B phases with sawtooth morphology. The FeB/Fe2B volume ratio was higher in the specimens borided with NB. The thickness of the boride layer (FeB + Fe2B) increased with the increasing boriding temperature and time. The FeB layer in the NB specimen displayed a (002) preferred orientation.
Citation - WoS: 10
Citation - Scopus: 9
Bright, Dark, and Singular Optical Soliton Solutions for Perturbed Gerdjikov-Ivanov Equation
(Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Kumar, Sunil; Ulutas, Esma
This study consider Gerdjikov-Ivanov equation where the perturbation terms appear with full non-linearity. The Jacobi elliptic function ansatz method is implemented to obtain exact solutions of this equation that models pulse dynamics in optical fibers. It is retrieved some bright, dark optical and singular solitons profile in the limiting cases of the Jacobi elliptic functions. The constraint conditions depending on the parameters for the existence of solitons are also presented.
Citation - WoS: 23
Citation - Scopus: 27
Chemometric Approach To Simultaneous Chromatographic Determination of Paracetamol and Chlorzoxazone in Tablets and Spiked Human Plasma
(Taylor & Francis inc, 2006) Ozdemir, A; Aksoy, H; Baleanu, D; Dinç, E
New chemometric approaches were introduced into the high performance liquid chromatographic (HPLC) determination of chlorzoxazone (CZX) and paracetamol (PAR) in the tablets and spiked human plasma. These chemometric approaches contain the application of classical least squares (CLS), principle component regression (PCR), and partial least squares (PLS) calibrations to the multiwavelength HPLC peak area obtained by plotting the chromatograms at the five wavelengths. The multichromatograms were obtained by using the photodiode array detector at 225 (A), 240 (B), 255 (C), 270 (D), and 285 (E) nm. The algorithms of CLS, PCR, and PLS were applied to the multichromatogram data to construct the HPLC-CLS, HPLC-PCR, and HPLC-PLS calibrations. A mixture of acetonitrile and 0.1 M ammonium carbonate (60:40, v/v) on a Waters Symmetry (R) trademark C18 Column 5 mu m 4.6 x 250 mm at a flow rate of 0.8 mL/min was used as a mobile phase to separate and determine CZX and PAR in samples. Hydrochlorothiazide (IS) was used as an internal standard in this chromatographic separation. The HPLC chemometric calibrations were successfully applied to the quantitative analysis of the investigated drugs in commercial pharmaceutical preparation and spiked human plasma samples with high precision and accuracy.
Chemometric Calibration Based on the Wavelet Transform for the Quantitative Resolution of Two-Colorant Mixtures
(Editura Acad Romane, 2005) Baleanu, Dumitru; Dinç, E; Baleanu, D; Taş, Kenan; Üstundag, O; Tas, K; Matematik
In this study we proposed a wavelet transform (WT) followed by two chemometric techniques for the quantitative determination of sunset yellow (SUN) and tartrazine (TAR) in their market samples. Absorbances of the concentration set formed by TAR and SUN mixtures were measured between 335-575 nm at 480 points with 0.5 nm intervals and their absorbance values as absorbance data vectors were transferred into the wavelets domain. A continuous wavelet transform (CWT) was applied, to the absorbance data. The obtained CWT-coefficients (x-block) and concentration set (y-block) were used for the construction of the principal component regression (VCR) and partial least squares (PLS) calibrations. Good results were reported for the application of the combining wavelets and chemometric tools in the determination of colorants in samples.
Citation - WoS: 5
Citation - Scopus: 6
Coincidence Point Theorem on Hilbert Spaces Via Weak Ekeland Variational Principle and Application To Boundary Value Problem
(Chiang Mai Univ, Fac Science, 2021) Asadi, Mehdi; Karapınar, Erdal; Karapinar, Erdal; Matematik
In this paper, we give a new coincidence point theorem for two operators on Hilbert spaces for certain operators by using the weak Ekeland variational principle. Our paper extends and improves the results on the topic in the literature. We consider a boundary value problem as an application of our results.
Citation - WoS: 5
Citation - Scopus: 9
Combined Application of Continuous Wavelet Transform-Zero Crossing Technique in the Simultaneous Spectrophotometric Determination of Perindopril and Indapamid in Tablets
(Soc Brasileira Quimica, 2009) Pektas, Goezde; Baleanu, Dumitru; Dinc, Erdal; Baleanu, Dumitru; Matematik
Signal processing methods based on the combined use of the continuous wavelet transform (CWT) and zero-crossing technique were applied to the simultaneous spectrophotometric determination of perindopril (PER) and indapamide (IND) in tablets. These signal processing methods do not require any priory separation step. Initially, various wavelet families were tested to identify the optimum signal processing giving the best recovery results. From this procedure, the Haar and Biorthogonal 1.5 continuous wavelet transform (HAAR-CWT and BIOR 1.5-CWT, respectively) were found suitable for the analysis of the related compounds. After transformation of the absorbance vectors by using HAAR-CWT and BIOR 1.5-CWT, the CWT-coefficients were drawn as a graph versus wavelength and then the HAAR-CWT and BIOR 1.5-CWT spectra were obtained. Calibration graphs for PER and IND were obtained by measuring the CWT amplitudes at 231.1 and 291.0 rim in the HAAR-CWT spectra and at 228.5 and 246.8 nm in BIOR 1.5-CWT spectra. respectively. In order to compare the performance of HAAR-CWT and BIOR 1.5-CWT approaches, derivative spectrophotometric (DS) method and HPLC as comparison methods, were applied to the PER-IND samples. In this DS method, first derivative absorbance values at 221.6 for PER and 282.7 nm for IND were used to obtain the calibration graphs. The validation of the CWT and DS signal processing methods was carried out by using the recovery study and standard addition technique. In the following step, these methods were Successfully applied to the commercial tablets containing PER and IND compounds and good accuracy and precision were reported for the experimental results obtained by all proposed signal processing methods.
Citation - WoS: 16
Citation - Scopus: 16
Comparative Application of Wavelet Approaches To Absorption and Ratio Spectra for the Simultaneous Determination of Diminazene Aceturate and Phenazone in Veterinary Granules for Injection
(Govi-verlag Pharmazeutischer verlag Gmbh, 2005) Dinç, E; Baleanu, Dumitru; Kanbur, M; Baleanu, D; Matematik
A comparison of two wavelet approaches, Daubechies and reverse Biorthogonal, is described for the quantitative resolution of a binary mixture of diminazene aceturate (DIMA) and phenazone (PHE) in veterinary granules for injection without any chemical separation. These two approaches were specified as db4 (a = 180) and rbior3.7 (a = 125) respectively, after testing the signal analysis parameters for the overlapping absorption spectra and ratio spectra. In the first step db4 (a = 180) was applied to the original absorbance data vector of DIMA and PHE. In the second step rbio3.7 (a = 125) was applied to the ratio spectra data vectors of DIMA using the divisor PHE. The same approach was also subjected to the ratio spectra of PHE using the divisor DIMA. The db4 (a = 180) and rbior3.7 (a = 125) calibration graphs were constructed using the transformation values obtained in the wavelet domain. In the method validation, the wavelet calibration functions were tested using synthetic mixtures and the standard addition technique. The simultaneous quantitative analysis of DIMA and PHE in the commercial veterinary preparation was achieved by the elaborated methods. The assay results were compared with each other and good agreement was observed.

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