Browsing by Author "Jena, Rajarama Mohan"

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Citation - WoS: 13
Citation - Scopus: 13
Analysis of Time-Fractional Dynamical Model of Romantic and Interpersonal Relationships With Non-Singular Kernels: a Comparative Study
(Wiley, 2021) Chakraverty, Snehashish; Baleanu, Dumitru; Jena, Subrat Kumar; Jena, Rajarama Mohan
The analysis of interpersonal relationships has started to become popular in the last few decades. Interpersonal relationships exist in many ways, including family, friendship, job, and clubs. In this manuscript, we have implemented the homotopy perturbation Elzaki transform method to obtain the solutions of romantic and interpersonal relationships model involving time-fractional-order derivatives with non-singular kernels. The present method is the combination of the classical homotopy perturbation method and the Elzaki transform. This method offers a rapidly convergent series of solutions. The present approach explores the dynamics of love between couples. Validation and usefulness of the method are incorporated with new fractional-order derivatives with exponential decay law and with general Mittag-Leffler law. Obtained results are compared with the established solution defined in the Caputo sense. Further, a comparative study among Caputo and newly defined fractional derivatives are discussed.
Citation - WoS: 41
Citation - Scopus: 46
A Novel Analytical Technique for the Solution of Time-Fractional Ivancevic Option Pricing Model
(Elsevier, 2020) Chakraverty, Snehashish; Baleanu, Dumitru; Jena, Rajarama Mohan
The Ivancevic option pricing model is an alternative of the standard Black-Scholes pricing equation, which signifies a controlled Brownian motion related to the nonlinear Schrodinger equation. Even though many researchers have studied the applicability and practicality of this model, but the analytical approach of this model is rarely found in the literature. In this paper, a novel semi-analytical technique called fractional reduced differential transform method has been applied to solve the Schrodinger type option pricing model, which is characterized by the time-fractional derivative. Two problems are explained to validate and prove the effectiveness of the proposed technique. Obtained results are compared with the solution of other existing methods for a particular case. This comparison shows that the attained results are in good agreement with the existing solutions. (C) 2020 Published by Elsevier B.V.
Citation - WoS: 26
Citation - Scopus: 33
On New Solutions of Time-Fractional Wave Equations Arising in Shallow Water Wave Propagation
(Mdpi, 2019) Chakraverty, Snehashish; Baleanu, Dumitru; Jena, Rajarama Mohan
The primary objective of this manuscript is to obtain the approximate analytical solution of Camassa-Holm (CH), modified Camassa-Holm (mCH), and Degasperis-Procesi (DP) equations with time-fractional derivatives labeled in the Caputo sense with the help of an iterative approach called fractional reduced differential transform method (FRDTM). The main benefits of using this technique are that linearization is not required for this method and therefore it reduces complex numerical computations significantly compared to the other existing methods such as the perturbation technique, differential transform method (DTM), and Adomian decomposition method (ADM). Small size computations over other techniques are the main advantages of the proposed method. Obtained results are compared with the solutions carried out by other technique which demonstrates that the proposed method is easy to implement and takes small size computation compared to other numerical techniques while dealing with complex physical problems of fractional order arising in science and engineering.
Citation - WoS: 20
Citation - Scopus: 24
On the Solution of an Imprecisely Defined Nonlinear Time-Fractional Dynamical Model of Marriage
(Mdpi, 2019) Chakraverty, Snehashish; Baleanu, Dumitru; Jena, Rajarama Mohan
The present paper investigates the numerical solution of an imprecisely defined nonlinear coupled time-fractional dynamical model of marriage (FDMM). Uncertainties are assumed to exist in the dynamical system parameters, as well as in the initial conditions that are formulated by triangular normalized fuzzy sets. The corresponding fractional dynamical system has first been converted to an interval-based fuzzy nonlinear coupled system with the help of a single-parametric gamma-cut form. Further, the double-parametric form (DPF) of fuzzy numbers has been used to handle the uncertainty. The fractional reduced differential transform method (FRDTM) has been applied to this transformed DPF system for obtaining the approximate solution of the FDMM. Validation of this method was ensured by comparing it with other methods taking the gamma-cut as being equal to one.
Citation - WoS: 39
Citation - Scopus: 39
Sir Epidemic Model of Childhood Diseases Through Fractional Operators With Mittag-Leffler and Exponential Kernels
(Elsevier, 2021) Chakraverty, Snehashish; Baleanu, Dumitru; Jena, Rajarama Mohan
Vaccination programs for infants have significantly affected childhood morbidity and mortality. The primary goal of health administrators is to protect children against diseases that can be prevented by vaccination. In this manuscript, we have applied the homotopy perturbation Elzaki transform method to obtain the solutions of the epidemic model of childhood diseases involving time-fractional order Atangana-Baleanu and Caputo-Fabrizio derivatives. The present method is the combination of the classical homotopy perturbation method and the Elzaki transform. Although Elzaki transform is an effective method for solving fractional differential equations, this method sometimes fails to handle nonlinear terms from the fractional differential equations. These difficulties may be overcome by coupling this transform with that of HPM. This method offers a rapidly convergent series solutions. Validation and usefulness of the technique are incorporated with new fractional-order derivatives with exponential decay law and with general Mittag-Leffler law. Obtained results are compared with the established solution defined in the Caputo sense. Further, a comparative study among Caputo, Atangana-Baleanu, and Caputo-Fabrizio derivatives is discussed. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.