Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
40 results
Search Results
Article Citation - WoS: 63Citation - Scopus: 76A Fractional Model of Convective Radial Fins With Temperature-Dependent Thermal Conductivity(Editura Acad Romane, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; MatematikThe principal purpose of the present article is to examine a fractional model of convective radial fins having constant and temperature-dependent thermal conductivity. In order to solve fractional order energy balance equation, a numerical algorithm namely homotopy analysis transform method is considered. The fin temperature is derived in terms of thermo-geometric fin parameter. Our method is not limited to the use of a small parameter, such as in the standard perturbation technique. The numerical simulation for temperature and fin tip temperature are presented graphically. The results can be used in thermal design to consider radial fins having both constant and temperature-dependent thermal conductivity.Article Citation - WoS: 22Citation - Scopus: 25New Approach on Controllability of Hilfer Fractional Derivatives With Nondense Domain(Amer inst Mathematical Sciences-aims, 2022) Jothimani, Kasthurisamy; Ravichandran, Chokkalingam; Baleanu, Dumitru; Kumar, Devendra; Nisar, Kottakkaran SooppyThis work picturizes the results on the controllability of the nondense Hilfer neutral fractional derivative (HNFD). The uniqueness and controllability of HNFD are discussed with Winch theorem and Banach contraction technique. In addition, a numerical approximation is given to deal with different criteria of our results.Article Citation - WoS: 12Citation - Scopus: 21Generalized Invexity and Duality in Multiobjective Variational Problems Involving Non-Singular Fractional Derivative(de Gruyter Poland Sp Z O O, 2022) Kumar, Devendra; Alshehri, Hashim M.; Singh, Jagdev; Baleanu, Dumitru; Dubey, Ved PrakashIn this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using the concept of weak minima. Multiobjective variational problems find their applications in economic planning, flight control design, industrial process control, control of space structures, control of production and inventory, advertising investment, impulsive control problems, mechanics, and several other engineering and scientific problems. The proposed work considers the newly derived Caputo-Fabrizio (CF) fractional derivative operator. It is actually a convolution of the exponential function and the first-order derivative. The significant characteristic of this fractional derivative operator is that it provides a non-singular exponential kernel, which describes the dynamics of a system in a better way. Moreover, the proposed work also presents various weak, strong, and converse duality theorems under the diverse generalized invexity conditions in view of the CF fractional derivative operator.Article Citation - WoS: 8Citation - Scopus: 9Numerical Simulation for Generalized Time-Fractional Burgers' Equation With Three Distinct Linearization Schemes(Asme, 2023) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Chawla, Reetika; Reetika, ChawlaIn the present study, we examined the effectiveness of three linearization approaches for solving the time-fractional generalized Burgers' equation using a modified version of the fractional derivative by adopting the Atangana-Baleanu Caputo derivative. A stability analysis of the linearized time-fractional Burgers' difference equation was also presented. All linearization strategies used to solve the proposed nonlinear problem are unconditionally stable. To support the theory, two numerical examples are considered. Furthermore, numerical results demonstrate the comparison of linearization strategies and manifest the effectiveness of the proposed numerical scheme in three distinct ways.Article Citation - WoS: 6Citation - Scopus: 4Novel Numerical Approach for Time Fractional Equations With Nonlocal Condition(Springer, 2024) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Taneja, KomalA numerical method for solving inhomogeneous nonlocal time fractional convection-diffusion-reaction equations with variable coefficients has been developed. The fractional time operator is taken in the sense of the modified operator with the Mittag-Leffler kernel. The numerical method is based on the modified Gauss elimination with Taylor's expansion. Through rigorous analysis, it has been proved that the given method is unconditionally stable and second-order convergent in space and time. The numerical results for three test problems illustrate the efficiency and validity of the theoretical estimates.Article Citation - WoS: 8Citation - Scopus: 14Analysis 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, RavindraThe 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.Article Citation - WoS: 1Citation - Scopus: 1A Higher-Order Approach for Time-Fractional Generalized Burgers' Equation(World Scientific Publ Co Pte Ltd, 2023) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Taneja, KomalA fast higher-order scheme is established for solving inhomogeneous time-fractional generalized Burgers' equation. The time-fractional operator is taken as the modified operator with the Mittag-Leffler kernel. Through stability analysis, it has been demonstrated that the proposed numerical approach is unconditionally stable. The convergence of the numerical method is analyzed theoretically using von Neumann's method. It has been proved that the proposed numerical method is fourth-order convergent in space and second-order convergent in time in the L-2-norm. The scheme's proficiency and effectiveness are examined through two numerical experiments to validate the theoretical estimates. The tabular and graphical representations of numerical results confirm the high accuracy and versatility of the scheme.Article Citation - WoS: 15Citation - Scopus: 19New Aspects of Fractional Bloch Model Associated With Composite Fractional Derivative(Edp Sciences S A, 2021) Kumar, Devendra; Baleanu, Dumitru; Singh, JagdevThis paper studies a fractional Bloch equation pertaining to Hilfer fractional operator. Bloch equation is broadly applied in physics, chemistry, nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI) and many more. The sumudu transform technique is applied to obtain the analytic solutions for nuclear magnetization M = (M-x, M-y, M-z). The general solution of nuclear magnetization M is shown in the terms of Mittag-Leffler (ML) type function. The influence of order and type of Hilfer fractional operator on nuclear magnetization M is demonstrated in graphical form. The study of Bloch equation with composite fractional derivative reveals the new features of Bloch equation. The discussed fractional Bloch model provides crucial and applicable results to introduce novel information in scientific and technological fields.Article Citation - WoS: 38Citation - Scopus: 44Fractional Klein-Gordon Equations With Mittag-Leffler Memory(Elsevier, 2020) Prakasha, D. G.; Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru; Veeresha, P.The main objective of the present investigation is to find the solution for the fractional model of Klein-Gordon-Schrodinger system with the aid of q-homotopy analysis transform method (q-HATM). The projected solution procedure is an amalgamation of q-HAM with Laplace transform. More preciously, to elucidate the effectiveness of the projected scheme we illustrate the response of the q-HATM results, and the numerical simulation is offered to guarantee the exactness. Further, the physical behaviour has been presented associated with parameters present the method with respect fractional-order. The present study confirms that, the projected solution procedure is highly methodical and accurate to solve and study the behaviours of the system of differential equations with arbitrary order exemplifying the real word problems.Editorial Citation - WoS: 2Citation - Scopus: 3Editorial Note on the Special Issue: "fractional Calculus Models for the Dynamics of Complex Systems(Elsevier, 2021) Kumar, Devendra; Pinto, Carla M. A.; Baleanu, Dumitru; Sweilam, Nasser H.