Browsing by Author "Jena, Rajarama Mohan"

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Citation Count: Jena, R.M.; Chakraverty, S.; Baleanu, D.,"A Novel Analytical Technique for the Solution of Time-Fractional Ivancevic Option Pricing Model", Physica A: Statistical Mechanics and Its Applications, Vol. 550, (2020).
A Novel Analytical Technique for the Solution of Time-Fractional Ivancevic Option Pricing Model
(Elsevier B.V., 2020) Jena, Rajarama Mohan; Chakraverty, S.; Baleanu, Dumitru; 56389
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.
Citation Count: Jena, Rajarama Mohan...et al. (2021). "A robust technique based solution of time-fractional seventh-order Sawada-Kotera and Lax's KdV equations", Modern Physics Letters B, Vol. 35, No. 16.
A robust technique based solution of time-fractional seventh-order Sawada-Kotera and Lax's KdV equations
(2021) Jena, Rajarama Mohan; Chakraverty, Snehashish; Baleanu, Dumitru; Adel, Waleed; Rezazadeh, Hadi; 56389
In this paper, the fractional reduced differential transform method (FRDTM) is used to obtain the series solution of time-fractional seventh-order Sawada-Kotera (SSK) and Lax's KdV (LKdV) equations under initial conditions (ICs). Here, the fractional derivatives are considered in the Caputo sense. The results obtained are contrasted with other previous techniques for a specific case, alpha = 1 revealing that the presented solutions agree with the existing solutions. Further, convergence analysis of the present results with an increasing number of terms of the solution and absolute error has also been studied. The behavior of the FRDTM solution and the effects on different values alpha are illustrated graphically. Also, CPU-time taken to obtain the solutions of the title problems using FRDTM has been demonstrated.
Citation Count: Jena, Rajarama Mohan...et al. (2021). "Analysis of time-fractional dynamical model of romantic and interpersonal relationships with non-singular kernels: A comparative study", Mathematical Methods in the Applied Sciences, Vol. 44, No. 2, pp. 2183-2199.
Analysis of time-fractional dynamical model of romantic and interpersonal relationships with non-singular kernels: A comparative study
(2021) Jena, Rajarama Mohan; Chakraverty, Snehashish; Baleanu, Dumitru; Jena, Subrat Kumar; 56389
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 Count: Jena, Rajarama Mohan...et al. (2020). "New Aspects of ZZ Transform to Fractional Operators With Mittag-Leffler Kernel", Frontiers in Physics, Vol. 8.
New Aspects of ZZ Transform to Fractional Operators With Mittag-Leffler Kernel
(2020) Jena, Rajarama Mohan; Chakraverty, Snehashish; Baleanu, Dumitru; Alqurashi, Maysaa M.; 56389
In this paper, we discuss the relationship between the Zain Ul Abadin Zafar (ZZ) transform with Laplace and Aboodh transforms. Further, the ZZ transform is applied to the fractional derivative with the Mittag-Leffler kernel defined in both the Caputo and Riemann-Liouville sense. In order to illustrate the validity and applicability of the transform, we solve some illustrative examples. © Copyright © 2020 Jena, Chakraverty, Baleanu and Alqurashi.
Citation Count: Jena, Rajarama Mohan; Chakraverty, Snehashish; Baleanu, Dumitru, "On New Solutions of Time-Fractional Wave Equations Arising in Shallow Water Wave Propagation", Mathematics, Vol. 7, No. 8, (Agust 2019).
On New Solutions of Time-Fractional Wave Equations Arising in Shallow Water Wave Propagation
(MDPI, 2019) Jena, Rajarama Mohan; Chakraverty, Snehashish; Baleanu, Dumitru; 56389
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 Count: Jena, Rajarama Mohan; Chakraverty, Snehashish; Baleanu, Dumitru, "On the Solution of an Imprecisely Defined Nonlinear Time-Fractional Dynamical Model of Marriage", Mathematics, Vol.7, No. 8, (Agust 2019).
On the Solution of an Imprecisely Defined Nonlinear Time-Fractional Dynamical Model of Marriage
(MDPI, 2019) Jena, Rajarama Mohan; Chakraverty, Snehashish; Baleanu, Dumitru; 56389
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 Count: Jena, Rajarama Mohan; Chakraverty, Snehashish; Baleanu, Dumitru (2021). "SIR epidemic model of childhood diseases through fractional operators with Mittag-Leffler and exponential kernels", Mathematics and Computers in Simulation, Vol. 182, pp. 514-534.
SIR epidemic model of childhood diseases through fractional operators with Mittag-Leffler and exponential kernels
(2021) Jena, Rajarama Mohan; Chakraverty, Snehashish; Baleanu, Dumitru; 56389
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.
Citation Count: Jena, Rajarama Mohan; Chakraverty, Snehashish; Baleanu, Dumitru (2020). "Solitary wave solution for a generalized Hirota-Satsuma coupled KdV and MKdV equations: A semi-analytical approach", Alexandria Engineering Journal, Vol. 59, No. 5, pp. 2877-2889.
Solitary wave solution for a generalized Hirota-Satsuma coupled KdV and MKdV equations: A semi-analytical approach
(2020) Jena, Rajarama Mohan; Chakraverty, Snehashish; Baleanu, Dumitru; 56389
Nonlinear fractional differential equations (NFDEs) offer an effective model of numerous phenomena in applied sciences such as ocean engineering, fluid mechanics, quantum mechanics, plasma physics, nonlinear optics. Some studies in control theory, biology, economy, and electrodynamics, etc. demonstrate that NFDEs play the primary role in explaining various phenomena arising in real-life. Now-a-day NFDEs in various scientific fields in particular optical fibers, chemical physics, solid-state physics, and so forth have the most important subjects for study. Finding exact responses to these equations will help us to a better understanding of our environmental nonlinear physical phenomena. In this regard, in the present study, we have applied fractional reduced differential transform method (FRDTM) to obtain the solution of nonlinear time-fractional Hirota-Satsuma coupled KdV and MKdV equations. The novelty of the FRDTM is that it does not require any discretization, transformation, perturbation, or any restrictive conditions. Moreover, this method requires less computation compared to other methods. Computed results are compared with the existing results for the special cases of integer order. The present results are in good agreement with the existing solutions. Here, the fractional derivatives are considered in the Caputo sense. The presented method is a semi-analytical method based on the generalized Taylor series expansion and yields an analytical solution in the form of a polynomial.