PubMed İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8650

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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: 110
Citation - Scopus: 112
Active Laser Radar Systems With Stochastic Electromagnetic Beams in Turbulent Atmosphere
(Optica Publishing Group, 2008) Cai, Yangjian; Korotkova, Olga; Eyyuboglu, Halil T.; Baykal, Yahya; 7688; 7812; 06.02. Elektronik ve Haberleşme Mühendisliği; 06.03. Elektrik-Elektronik Mühendisliği; 06. Mühendislik Fakültesi; 01. Çankaya Üniversitesi
Propagation of stochastic electromagnetic beams through paraxial ABCD optical systems operating through turbulent atmosphere is investigated with the help of the ABCD matrices and the generalized Huygens-Fresnel integral. In particular, the analytic formula is derived for the cross-spectral density matrix of an electromagnetic Gaussian Schell-model (EGSM) beam. We applied our analysis for the ABCD system with a single lens located on the propagation path, representing, in a particular case, the unfolded double-pass propagation scenario of active laser radar. Through a number of numerical examples we investigated the effect of local turbulence strength and lens' parameters on spectral, coherence and polarization properties of the EGSM beam. (C) 2008 Optical Society of America
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: 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: 12
Analysis of Dengue Transmission Dynamic Model by Stability and Hopf Bifurcation With Two-Time Delays
(Imr Press, 2023) Ambalarajan, Venkatesh; Sivakumar, Vinoth; Dhandapani, Prasantha Bharathi; Baleanu, Dumitru; Murugadoss, Prakash Raj; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Background: Mathematical models reflecting the epidemiological dynamics of dengue infection have been discovered dating back to 1970. The four serotypes (DENV-1 to DENV-4) that cause dengue fever are antigenically related but different viruses that are transmitted by mosquitoes. It is a significant global public health issue since 2.5 billion individuals are at risk of contracting the virus. Methods: The purpose of this study is to carefully examine the transmission of dengue with a time delay. A dengue transmission dynamic model with two delays, the standard incidence, loss of immunity, recovery from infectiousness, and partial protection of the human population was developed. Results: Both endemic equilibrium and illness-free equilibrium were examined in terms of the stability theory of delay differential equations. As long as the basic reproduction number (R0) is less than unity, the illness-free equilibrium is locally asymptotically stable; however, when R0 exceeds unity, the equilibrium becomes unstable. The existence of Hopf bifurcation with delay as a bifurcation parameter and the conditions for endemic equilibrium stability were examined. To validate the theoretical results, numerical simulations were done. Conclusions: The length of the time delay in the dengue transmission epidemic model has no effect on the stability of the illness-free equilibrium. Regardless, Hopf bifurcation may occur depending on how much the delay impacts the stability of the underlying equilibrium. This mathematical modelling is effective for providing qualitative evaluations for the recovery of a huge population of afflicted community members with a time delay.
Citation - WoS: 66
Citation - Scopus: 86
Analysis of Fractional Model of Guava for Biological Pest Control With Memory Effect
(Elsevier, 2021) Ganbari, Behzad; Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Introduction: Fractional operators find their applications in several scientific and engineering processes. We consider a fractional guava fruit model involving a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. The fractional guava fruit model is considered as a Lotka-Volterra nature. Objectives: The main objective of this work is to study a guava fruit model associated with a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. Methods: Existence and uniqueness analysis of the solution is evaluated effectively by using Picard Lindelof approach. An approximate numerical solution of the fractional guava fruit problem is obtained via a numerical scheme. Results: The positivity analysis and equilibrium analysis for the fractional guava fruit model is discussed. The numerical results are demonstrated to prove our theoretical results. The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters is discussed. Conclusion: The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters shows new vista and interesting phenomena of the model. The results are indicating that the fractional approach with non-singular kernel plays an important role in the study of different scientific problems. The suggested numerical scheme is very efficient for solving nonlinear fractional models of physical importance. (C) 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
Citation - WoS: 183
Citation - Scopus: 193
Analysis of Reciprocity of Cos-Gaussian and Cosh-Gaussian Laser Beams in a Turbulent Atmosphere
(Optical Soc Amer, 2004) Eyyuboglu, HT; Baykal, Y; 7688; 7812; 06.02. Elektronik ve Haberleşme Mühendisliği; 06.03. Elektrik-Elektronik Mühendisliği; 06. Mühendislik Fakültesi; 01. Çankaya Üniversitesi
In a turbulent atmosphere, starting with a cos-Gaussian excitation at the source plane, the average intensity profile at the receiver plane is formulated. This average intensity profile is evaluated against the variations of link lengths, turbulence levels, two frequently used free-space optics wavelengths, and beam displacement parameters. We show that a cos-Gaussian beam, following a natural diffraction, is eventually transformed into a cosh-Gaussian beam. Combining our earlier results with the current findings, we conclude that cos-Gaussian and cosh-Gaussian beams act in a reciprocal manner after propagation in turbulence. The rates (paces) of conversion in the two directions are not the same. Although the conversion of cos-Gaussian beams to cosh-Gaussian beams can happen over a wide range of turbulence levels (low to moderate to high), the conversion of cosh-Gaussian beams to cos-Gaussian beams is pronounced under relatively stronger turbulence conditions. Source and propagation parameters that affect this reciprocity have been analyzed. (C) 2004 Optical Society of America.
Citation - WoS: 7
Citation - Scopus: 17
An Analysis on the Relationship Between Safety Awareness and Safety Behaviors of Healthcare Professionals, Ankara/Turkey
(Oxford Univ Press, 2020) Uzuntarla, Fatma; Kucukali, Serhat; Uzuntarla, Yasin; 20413; 06.05. İnşaat Mühendisliği; 06. Mühendislik Fakültesi; 01. Çankaya Üniversitesi
Objectives: This descriptive study aims to examine the relationship between the safety awareness of healthcare professional and their safety behaviors. Methods: The study was carried out on 418 healthcare professionals working in a training and research hospital in Ankara/Turkey. The survey method was used as data collection tool. The questionnaire consisted of 3 sections and 18 questions. First section consisted of questions on sociodemographic characteristics and, second section consisted of the awareness scale and third section consisted of safety behaviors scale. Results: The safety awareness and safety behaviors are scored on a scale from 1 (completely disagree) to 5 (completely agree). The safety awareness and safety behaviors has an average score of 3.85 +/- 0.81 and 3.56 +/- 0.82, respectively. The safety awareness and safety behavior levels of healthcare professionals were found to be high. Conclusion: A significant positive correlation was found between safety awareness and safety behaviors and it was concluded that the increase in safety awareness led to an increase in safety behavior.
Analytical Results for Positivity of Discrete Fractional Operators With Approximation of the Domain of Solutions
(Amer inst Mathematical Sciences-aims, 2022) O'Regan, Donal; Baleanu, Dumitru; Hamed, Y. S.; Elattar, Ehab E.; Mohammed, Pshtiwan Othman; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We study the monotonicity method to analyse nabla positivity for discrete fractional operators of Riemann-Liouville type based on exponential kernels, where ((CFR)(c0)del F-theta)(t) > -epsilon Lambda(theta - 1) (del F)(c(0) + 1) such that (del F)(c(0) + 1) >= 0 and epsilon > 0. Next, the positivity of the fully discrete fractional operator is analyzed, and the region of the solution is presented. Further, we consider numerical simulations to validate our theory. Finally, the region of the solution and the cardinality of the region are discussed via standard plots and heat map plots. The figures confirm the region of solutions for specific values of epsilon and theta.
Citation - WoS: 18
Citation - Scopus: 20
Antecedents of Problematic Social Media Use and Cyberbullying Among Adolescents: Attachment, the Dark Triad and Rejection Sensitivity
(Springer, 2023) Demircioglu, Zeynep Isil; Goncu-Kose, Asli; 166202; 01. Çankaya Üniversitesi; 02. Fen-Edebiyat Fakültesi; 02.04. Psikoloji
With the acceleration of internet use, problematic social media use (PSMU) is included in our lives. When looking at the antecedents of PSMU, being young has been found to be a risk factor for PSMU. In addition to the benefits of technological advances in education and training, rapid technological developments may also result in problematic behaviors, especially among children and young. Recently, possibilities brought by technology and more widespread use of technology by young people have created a new concept, namely, cyberbullying. The present study aims to examine the effects of attachment anxiety and avoidance on PSMU and cyberbullying as with the partial mediating effects of the Dark Triad personality traits, angry rejection sensitivity, and anxious rejection sensitivity among adolescents. In general, the findings supported the proposed theoretical model. The results are discussed in terms of theoretical and practical implications along with suggestions for future research.
Citation - WoS: 32
Citation - Scopus: 36
Attentional Control Is Partially Impaired in Obstructive Sleep Apnea Syndrome
(Wiley, 2013) Atalay, Nart Bedin; Kanat, Fikret; Suerdem, Mecit; Tulek, Baykal; 102366; 02.04. Psikoloji; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Obstructive sleep apnea syndrome is associated with executive cognitive impairment. An important question is whether impairment in executive functioning in obstructive sleep apnea syndrome is independent of dysfunction in attention. Attentional control is a subcomponent of executive functioning that is mediated by frontal lobe processing. In the current study, we investigated whether attentional control is deficient in obstructive sleep apnea syndrome. Attentional control processes were investigated through conflict adaptation and conflict frequency paradigms. These neuropsychological paradigms were assessed by using the Simon, Flanker and Stroop tasks. We additionally analysed post-error slowing data within these tasks. Error processing is another index of cognitive control that is mediated by frontal lobe functioning. Our sample consisted of 14 healthy adults and 24 patients with untreated moderate-severe obstructive sleep apnea syndrome. Results indicated that attentional control is partially dysfunctional among patients with obstructive sleep apnea syndrome. Attentional control processes were deficient when focal attention (Flanker task) processes were involved, but were intact when observed using the Simon and Stroop tasks. A non-significant trend in post-error slowing data suggested that error processing, assessed with the Flanker task, was diminished among patients with obstructive sleep apnea syndrome. These results support the view that obstructive sleep apnea syndrome leads to some amount of frontal lobe dysfunction, and that attentional control and error processing might be particularly affected by obstructive sleep apnea syndrome.
Citation - WoS: 37
Citation - Scopus: 49
Automated Classification of Rheumatoid Arthritis, Osteoarthritis, and Normal Hand Radiographs With Deep Learning Methods
(Springer, 2022) Maras, Hadi Hakan; Ureten, Kemal; 34410; 06.01. Bilgisayar Mühendisliği; 06. Mühendislik Fakültesi; 01. Çankaya Üniversitesi
Rheumatoid arthritis and hand osteoarthritis are two different arthritis that causes pain, function limitation, and permanent joint damage in the hands. Plain hand radiographs are the most commonly used imaging methods for the diagnosis, differential diagnosis, and monitoring of rheumatoid arthritis and osteoarthritis. In this retrospective study, the You Only Look Once (YOLO) algorithm was used to obtain hand images from original radiographs without data loss, and classification was made by applying transfer learning with a pre-trained VGG-16 network. The data augmentation method was applied during training. The results of the study were evaluated with performance metrics such as accuracy, sensitivity, specificity, and precision calculated from the confusion matrix, and AUC (area under the ROC curve) calculated from ROC (receiver operating characteristic) curve. In the classification of rheumatoid arthritis and normal hand radiographs, 90.7%, 92.6%, 88.7%, 89.3%, and 0.97 accuracy, sensitivity, specificity, precision, and AUC results, respectively, and in the classification of osteoarthritis and normal hand radiographs, 90.8%, 91.4%, 90.2%, 91.4%, and 0.96 accuracy, sensitivity, specificity, precision, and AUC results were obtained, respectively. In the classification of rheumatoid arthritis, osteoarthritis, and normal hand radiographs, an 80.6% accuracy result was obtained. In this study, to develop an end-to-end computerized method, the YOLOv4 algorithm was used for object detection, and a pre-trained VGG-16 network was used for the classification of hand radiographs. This computer-aided diagnosis method can assist clinicians in interpreting hand radiographs, especially in rheumatoid arthritis and osteoarthritis.
Citation - WoS: 53
Citation - Scopus: 58
Average Intensity and Spreading of an Elegant Hermite-Gaussian Beam in Turbulent Atmosphere
(Optical Soc Amer, 2009) Yuan, Yangsheng; Cai, Yangjian; Qu, Jun; Eyyuboglu, Halil T.; Baykal, Yahya; 7688; 7812; 06.02. Elektronik ve Haberleşme Mühendisliği; 06.03. Elektrik-Elektronik Mühendisliği; 06. Mühendislik Fakültesi; 01. Çankaya Üniversitesi
The propagation of an elegant Hermite-Gaussian beam (EHGB) in turbulent atmosphere is investigated. Analytical propagation formulae for the average intensity and effective beam size of an EHGB in turbulent atmosphere are derived based on the extended Huygens-Fresnel integral. The corresponding results of a standard Hermite-Gaussian beam (SHGB) in turbulent atmosphere are also derived for the convenience of comparison. The intensity and spreading properties of EHGBs and SHGBs in turbulent atmosphere are studied numerically and comparatively. It is found that the propagation properties of EHGBs and SHGBs are much different from their properties in free space, and the EHGB and SHGB with higher orders are less affected by the turbulence. What's more, the SHGB spreads more rapidly than the EHGB in turbulent atmosphere under the same conditions. Our results will be useful in long-distance free-space optical communications. (C) 2009 Optical Society of America
Citation - WoS: 113
Citation - Scopus: 115
Average Irradiance and Polarization Properties of a Radially or Azimuthally Polarized Beam in a Turbulent Atmosphere
(Optical Soc Amer, 2008) Cai, Yangjian; Lin, Qiang; Eyyuboglu, Halil T.; Baykal, Yahya; 7688; 7812; 06.02. Elektronik ve Haberleşme Mühendisliği; 06.03. Elektrik-Elektronik Mühendisliği; 06. Mühendislik Fakültesi; 01. Çankaya Üniversitesi
Analytical formulas are derived for the average irradiance and the degree of polarization of a radially or azimuthally polarized doughnut beam (PDB) propagating in a turbulent atmosphere by adopting a beam coherence-polarization matrix. It is found that the radial or azimuthal polarization structure of a radially or azimuthally PDB will be destroyed (i.e., a radially or azimuthally PDB is depolarized and becomes a partially polarized beam) and the doughnut beam spot becomes a circularly Gaussian beam spot during propagation in a turbulent atmosphere. The propagation properties are closely related to the parameters of the beam and the structure constant of the atmospheric turbulence. (C) 2008 Optical Society of America.
Citation - WoS: 23
Citation - Scopus: 26
Bi-Objective Adaptive Large Neighborhood Search Algorithm for the Healthcare Waste Periodic Location Inventory Routing Problem
(Springer Heidelberg, 2022) Aydemir-Karadag, Ayyuce; 116059; 01. Çankaya Üniversitesi
There has been an unexpected increase in the amount of healthcare waste during the COVID-19 pandemic. Managing healthcare waste is vital, as improper practices in the waste system can lead to the further spread of the virus. To develop effective and sustainable waste management systems, decisions in all processes from the source of the waste to its disposal should be evaluated together. Strategic decisions involve locating waste processing centers, while operational decisions deal with waste collection. Although the periodic collection of waste is used in practice, it has not been studied in the relevant literature. This paper integrates the periodic inventory routing problem with location decisions for designing healthcare waste management systems and presents a bi-objective mixed-integer nonlinear programming model that minimizes operating costs and risk simultaneously. Due to the complexity of the problem, a two-step approach is proposed. The first stage provides a mixed-integer linear model that generates visiting schedules to source nodes. The second stage offers a Bi-Objective Adaptive Large Neighborhood Search Algorithm (BOALNS) that processes the remaining decisions considered in the problem. The performance of the algorithm is tested on several hypothetical problem instances. Computational analyses are conducted by comparing BOALNS with its other two versions, Adaptive Large Neighborhood Search Algorithm and Bi-Objective Large Neighborhood Search Algorithm (BOLNS). The computational experiments demonstrate that our proposed algorithm is superior to these algorithms in several performance evaluation metrics. Also, it is observed that the adaptive search engine increases the capability of BOALNS to achieve high-quality Pareto-optimal solutions.
Citation - WoS: 19
Citation - Scopus: 19
Bipolar Intuitionistic Fuzzy Graph Based Decision-Making Model To Identify Flood Vulnerable Region
(Springer Heidelberg, 2023) Augustin, Felix; Narayanamoorthy, Samayan; Ahmadian, Ali; Balaenu, Dumitru; Kang, Daekook; Nithyanandham, Deva; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Bipolar intuitionistic fuzzy graphs (BIFG) are an extension of fuzzy graphs that can effectively capture uncertain or imprecise information in various applications. In graph theory, the covering, matching, and domination problems are benchmark concepts applied to various domains. These concepts may not be defined precisely using a crisp graph when the vertices and edges are more uncertain. Therefore, this study defines the covering, matching and domination concepts in bipolar intuitionistic fuzzy graphs (BIFG) using effective edges with certain important results. To define these concepts when the effective edges are absent, some novel approaches are discussed. To illustrate the domination concepts, the applications in disaster management and location selection problems are discussed. Further, a BIFG-based decision-making model is designed to identify the flood-vulnerable zones in Chennai, where the city's most and least vulnerable zones are identified. From the proposed model, Kodambakkam (Z(10)) is the most susceptible zone in Chennai. Finally, a comparative analysis is done with the existing techniques to show the efficiency of the model.
Citation - WoS: 24
Citation - Scopus: 30
Boger Nanofluid: Significance of Coriolis and Lorentz Forces on Dynamics of Rotating Fluid Subject To Suction/Injection Via Finite Element Simulation
(Nature Portfolio, 2022) Siddique, Imran; Hussain, Sajjad; Ali, Liaqat; Baleanu, Dumitru; Ali, Bagh; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This study briefings the roles of Coriolis, and Lorentz forces on the dynamics of rotating nanofluids flow toward a continuously stretching sheet. The nanoparticles are incorporated because of their unusual qualities like upgrade the thermal transportation, which are very important in heat exchangers, modern nanotechnology, electronics, and material sciences. The primary goal of this study is to improve heat transportation. Appropriate similarity transformations are applied for the principal PDEs to transform into nonlinear dimensionless PDEs. A widely recognized Numerical scheme known as the Finite Element Method is employed to solve the resultant convective boundary layer balances. Higher input in the solvent fraction parameter has a rising effect on the primary velocity and secondary velocity magnitude, and decreasing impact on the distributions of temperature. It is seen that growing contributions of the Coriolis, and Lorentz forces cause to moderate the primary and secondary velocities, but the temperature and concentration functions show opposite trend. The concentration, temperature, and velocities distributions for suction case is prominently than that of injection case, but inverse trend is observed for local Nusselt and Sherwood numbers. These examinations are relevant to the field of plastic films, crystal growing, paper production, heat exchanger, and bio-medicine.
Citation - WoS: 30
Citation - Scopus: 42
Caputo Sir Model for Covid-19 Under Optimized Fractional Order
(Springer, 2021) Ullah, Malik Z.; Baleanu, Dumitru; Alshomrani, Ali S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with 928,287 (14 September 2020) deaths within a couple of months. Ironically, 29,185,779 are still active cases. Having seen such a drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. The major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 1 April to 15 March 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam-Hyers and its generalized version. The best parameters have been obtained via the nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than the classical version of the SIR model (Brauer et al. in Mathematical Models in Epidemiology 2019). Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case (nu=1). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.
Citation - WoS: 8
Citation - Scopus: 9
Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions
(Hindawi Ltd, 2013) Agarwal, P.; Purohit, S. D.; Baleanu, D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We apply generalized operators of fractional integration involving Appell's function F-3(.) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdelyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.
Citation - WoS: 39
Citation - Scopus: 48
Chaotic Attractors With Fractional Conformable Derivatives in the Liouville-Caputo Sense and Its Dynamical Behaviors
(Mdpi, 2018) Baleanu, Dumitru; Tchier, Fairouz; Solis Perez, Jesus Emmanuel; Francisco Gomez-Aguilar, Jose; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and beta-conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and beta-conformable attractors are provided to illustrate the effectiveness of the proposed method.

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