WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
Browse
5 results
Search 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: 30Citation - Scopus: 38Modified Kawahara Equation Within a Fractional Derivative With Non-Singular Kernel(Vinca inst Nuclear Sci, 2018) Singh, Jagdev; Baleanu, Dumitru; Kumar, DevendraThe article addresses a time fractional modified Kawahara equation through a fractional derivative with exponential kernel. The Kawahara equation describes the generation of non-linear water-waves in the long-wavelength regime. The numerical solution of the fractional model of modified version of Kawahara equation is derived with the help of iterative scheme and the stability of applied technique is established. In order to demonstrate the usability and effectiveness of the new fractional derivative to describe water-waves in the long-wavelength regime, numerical results are presented graphically.Article Citation - WoS: 24Citation - Scopus: 25A New Fractional Model for Convective Straight Fins With Temperature-Dependent Thermal Conductivity(Vinca inst Nuclear Sci, 2018) Singh, Jagdev; Baleanu, Dumitru; Kumar, DevendraThe key aim of this work is to present a new non-integer model for convective straight fins with temperature-dependent thermal conductivity associated with Caputo-Fabrizio fractional derivative. The fractional energy balance equation is solved by using homotopy perturbation method coupled with Laplace transform method. The efficiency of straight fin has been derived in terms of thermo-geometric fin parameter. The numerical results derived by the application of suggested scheme are demonstrated graphically. The subsequent correlation equations are very helpful for thermal design scientists and engineers to design straight fins having temperature-dependent thermal conductivity.Article Citation - WoS: 31Citation - Scopus: 33Analysis of a New Fractional Model for Damped Bergers' Equation(de Gruyter Open Ltd, 2017) Kumar, Devendra; Al Qurashi, Maysaa; Baleanu, Dumitru; Singh, JagdevIn this article, we present a fractional model of the damped Bergers' equation associated with the Caputo-Fabrizio fractional derivative. The numerical solution is derived by using the concept of an iterative method. The stability of the applied method is proved by employing the postulate of fixed point. To demonstrate the effectiveness of the used fractional derivative and the iterative method, numerical results are given for distinct values of the order of the fractional derivative.Article Citation - WoS: 48Citation - Scopus: 52Analysis of Logistic Equation Pertaining To a New Fractional Derivative With Non-Singular Kernel(Sage Publications Ltd, 2017) Singh, Jagdev; Al Qurashi, Maysaa; Baleanu, Dumitru; Kumar, DevendraIn this work, we aim to analyze the logistic equation with a new derivative of fractional order termed in Caputo-Fabrizio sense. The logistic equation describes the population growth of species. The existence of the solution is shown with the help of the fixed-point theory. A deep analysis of the existence and uniqueness of the solution is discussed. The numerical simulation is conducted with the help of the iterative technique. Some numerical simulations are also given graphically to observe the effects of the fractional order derivative on the growth of population.