WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 11Citation - Scopus: 18Analysis of the family of integral equation involving incomplete types of I and Ī-functions(Taylor & Francis Ltd, 2023) Bhatter, Sanjay; Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Suthar, D.L.; Purohit, Sunil DuttThe present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete (Formula presented.) -function (I (Formula presented.) F) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (Formula presented.) -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.Article Citation - WoS: 5Citation - Scopus: 6Convoluted Fractional Differentials of Various Forms Utilizing the Generalized Raina's Function Description With Applications(Taylor & Francis Ltd, 2022) Baleanu, Dumitru; Ibrahim, Rabha W.A generalized differential operator utilizing Raina's function is constructed in light of a certain type of fractional calculus. We next use the generalized operators to build a formula for analytic functions of type normalized. Our method is based on the concepts of subordination and superordination. As an application, a class of differential equations involving the suggested operator is studied. As seen, the solution is provided by a certain hypergeometric function. We also create a fractional coefficient differential operator. Its geometric and analytic features are discussed. Finally, we use the Jackson's calculus to expand the Raina's differential operator and investigate its properties in relation to geometric function theory.Article Citation - WoS: 3Citation - Scopus: 4Towards an Earthquake-Resistant Architectural Design With the Image Classification Method(Taylor & Francis Ltd, 2024) Akan, Asli Er; Bingol, Kaan; Ormecioglu, Hilal Tugba; Er, Arzu; Ormecioglu, Tevfik Oguz; Er Akan, AslıArchitectural design is an interdisciplinary process which involves multiple stages that are interconnected. In this process, it is common for major decisions to be changed during the final stage, the analysis of the structural system. After making substantial corrections, the architect has to revisit the early stages, the preliminary project. This back-and-forth process can result in significant losses in time and cost. The proposed Irregularity Control Assistant (IC-Assistant) aims to provide architects with feedback on the conformity of structural system decisions to the irregularities defined in the Turkish Building Earthquake Code (TBEC-2018), using image processing methods at the early stages of the design process. The IC-Assistant was preliminarily created to evaluate the torsional irregularity of plan organization using deep learning methods. In this study, the results of the IC-Assistant were verified by structural analysis with the Prota-Structure program. The novelty of this study is the use of the image-classification method in earthquake-resistant architectural design. Up to this point, the method has been mainly used in facial recognition systems. This method minimizes time, human error, and cost losses and includes awareness of load bearing and earthquake resistance as inputs in the early stages of architectural design.Article Citation - WoS: 18Citation - Scopus: 20Comprehending the Model of Omicron Variant Using Fractional Derivatives(Taylor & Francis Ltd, 2023) Goswami, Pranay; Baleanu, Dumitru; Shankar Dubey, Ravi; Sharma, ShivaniThe world is grappled with an unprecedented challenges due to Corona virus. We are all battling this epidemic together, but we have not been able to defeat this epidemic yet. A new variant of this virus, named 'Omicron' is spreading these days. The fractional differential equations are providing us with better tools to study the mathematical model with memory effects. In this paper, we will consider an extended SER mathematical model with quarantined and vaccinated compartment to speculate the Omicron variant. This extended Susceptible Exposed Infected Recovered SER model involves equations that associate with the group of individuals those are susceptible (S), exposed (E): this class includes the individuals who are infected but not yet infectious, infectious (W): this class includes the individuals who are infected but not yet Quarantined, quarantined (Q): this class includes those group of people who are infectious, confirmed and quarantined, recovered (R) this class includes the group of individuals who have recovered, and vaccinated (V): this class includes the group of individuals who have been vaccinated. The non-negativity and of the extended SER model is analysed, the equilibrium points and the basic reproduction number are also calculated. The proposed model is then extended to the mathematical model using AB derivative operator. Proof for the existence and the uniqueness for the solution of fractional mathematical model in sense of AB fractional derivative is detailed and a numerical method is detailed to obtain the numerical solutions. Further we have discussed the efficiency of the vaccine against the Omicron variant via graphical representation.Article Citation - WoS: 11Citation - Scopus: 18Analysis of the Family of Integral Equation Involving Incomplete Types of I and (i)over-Bar(Taylor & Francis Ltd, 2023) Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Suthar, D. L.; Purohit, Sunil Dutt; Bhatter, SanjayThe present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (I/F) and an incomplete (I) over bar -function ((I/F) over bar) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (I) over bar -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.Article Citation - WoS: 13Citation - Scopus: 16A Generalized Study of the Distribution of Buffer Over Calcium on a Fractional Dimension(Taylor & Francis Ltd, 2023) Jangid, Kamlesh; Kumawat, Shyamsunder; Purohit, Sunil Dutt; Baleanu, Dumitru; Suthar, D. L.; Bhatter, SanjayCalcium is an essential element in our body and plays a vital role in moderating calcium signalling. Calcium is also called the second messenger. Calcium signalling depends on cytosolic calcium concentration. In this study, we focus on cellular calcium fluctuations with different buffers, including calcium-binding buffers, using the Hilfer fractional advection-diffusion equation for cellular calcium. Limits and start conditions are also set. By combining with intracellular free calcium ions, buffers reduce the cytosolic calcium concentration. The buffer depletes cellular calcium and protects against toxicity. Association, dissociation, diffusion, and buffer concentration are modelled. The solution of the Hilfer fractional calcium model is achieved through utilizing the integral transform technique. To investigate the influence of the buffer on the calcium concentration distribution, simulations are done in MATLAB 21. The results show that the modified calcium model is a function of time, position, and the Hilfer fractional derivative. Thus the modified Hilfer calcium model provides a richer physical explanation than the classical calcium model.Article Citation - WoS: 56Citation - Scopus: 59Nonlinear Generalized Fractional Differential Equations With Generalized Fractional Integral Conditions(Taylor & Francis Ltd, 2020) Ravichandran, Chokkalingam; Jarad, Fahd; Belmor, SamihaThis research work is dedicated to an investigation of the existence and uniqueness of a class of nonlinear psi-Caputo fractional differential equation on a finite interval , equipped with nonlinear psi-Riemann-Liouville fractional integral boundary conditions of different orders , we deal with a recently introduced psi-Caputo fractional derivative of order . The formulated problem will be transformed into an integral equation with the help of Green function. A full analysis of existence and uniqueness of solutions is proved using fixed point theorems: Leray-Schauder nonlinear alternative, Krasnoselskii and Schauder's fixed point theorems, Banach's and Boyd-Wong's contraction principles. We show that this class generalizes several other existing classes of fractional-order differential equations, and therefore the freedom of choice of the standard fractional operator. As an application, we provide an example to demonstrate the validity of our results.Article Citation - WoS: 17Citation - Scopus: 17Geometric Phase for Timelike Spherical Normal Magnetic Charged Particles Optical Ferromagnetic Model(Taylor & Francis Ltd, 2020) Korpinar, Zeliha; Inc, Mustafa; Baleanu, Dumitru; Korpinar, TalatWe introduce the theory of optical spherical Heisenberg ferromagnetic spin of timelike spherical normal magnetic flows of particles by the spherical frame in de Sitter space. Also, the concept of timelike spherical normal magnetic particles is investigated, which may have evolution equations. Afterward, we reveal new relationships with some integrability conditions for timelike spherical normal magnetic flows in de-Sitter space. In addition, we obtain total phases for spherical normal magnetic flows. We also acquire perturbed solutions of the nonlinear Schrodinger's equation that governs the propagation of solitons in de-Sitter space S-1(2). Finally, we provide some numerical simulations to supplement the analytical outcomes.Article Citation - WoS: 42Citation - Scopus: 56A Novel Jacobi Operational Matrix for Numerical Solution of Multi-Term Variable-Order Fractional Differential Equations(Taylor & Francis Ltd, 2020) Baleanu, D.; Agarwal, P.; El-Sayed, A. A.In this article, we introduce a numerical technique for solving a class of multi-term variable-order fractional differential equation.The method depends on establishing a shifted Jacobi operational matrix (SJOM) of fractional variable-order derivatives. By using the constructed (SJOM) in combination with the collocation technique, the main problem is reduced to an algebraic system of equations that can be solved numerically. The bound of the error estimate for the suggested method is investigated. Numerical examples are introduced to illustrate the applicability, generality, and accuracy of the proposed technique. Moreover, many physical applications problems that have the multi-term variable-order fractional differential equation formulae such as the damped mechanical oscillator problem and Bagley-Torvik equation can be solved via the presented method. Furthermore, the proposed method will be considered as a generalization of many numerical techniques.Article Citation - WoS: 8Citation - Scopus: 8Localization of Metallicity and Magnetic Properties of Graphene and of Graphene Nanoribbons Doped With Boron Clusters(Taylor & Francis Ltd, 2014) Kunstmann, Jens; Quandt, Alexander; Ozdogan, CemAs a possible way of modifying the intrinsic properties of graphene, we study the doping of graphene by embedded boron clusters with density functional theory. Cluster doping is technologically relevant as the cluster implantation technique can be readily applied to graphene. We find that B-7 clusters embedded into graphene and graphene nanoribbons are structurally stable and locally metallize the system. This is done both by the reduction of the Fermi energy and by the introduction of boron states near the Fermi level. A linear chain of boron clusters forms a metallic "wire" inside the graphene matrix. In a zigzag edge graphene nanoribbon, the cluster-related states tend to hybridize with the edge and bulk states. The magnetism in boron-doped graphene systems is generally very weak. The presence of boron clusters weakens the edge magnetism in zigzag edge graphene nanoribbon, rather than making the system appropriate for spintronics. Thus, the doping of graphene with the cluster implantation technique might be a viable technique to locally metallize graphene without destroying its attractive bulk properties.