Browsing by Author "Chakraverty, S."

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Citation - WoS: 24
Citation - Scopus: 32
Coupled Transform Method for Time-Space Fractional Black-Scholes Option Pricing Model
(Elsevier, 2020) Jena, R. M.; Chakraverty, S.; Baleanu, D.; Edeki, S. O.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper presents analytical solutions of a time-space-fractional Black-Scholes model (TSFBSM) using a coupled technique referred to as Fractional Complex Transform (FCT) with the aid of a modified differential transform method. The nature of the derivatives is in the sense of Jumarie. The considered cases and applications show more consistency of the TSFBSM with an actual integer and fractional data when compared with the classical Black-Scholes model. The method is noted to be very effective, even with little knowledge of fractional calculus. Extension of this to multi-factor models formulated in terms of stochastic dynamics is highly recommended. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
Citation - Scopus: 12
New Aspects of Zz Transform To Fractional Operators With Mittag-Leffler Kernel
(Frontiers Media SA, 2020) Chakraverty, S.; Baleanu, D.; Alqurashi, M.M.; Jena, R.M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - Scopus: 2
A Robust Technique Based Solution of Time-Fractional Seventh-Order Sawada-Kotera and Lax's Kdv Equations
(World Scientific, 2021) Chakraverty, S.; Baleanu, D.; Adel, W.; Rezazadeh, H.; Jena, R.M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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, α = 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 α are illustrated graphically. Also, CPU-time taken to obtain the solutions of the title problems using FRDTM has been demonstrated. © 2021 World Scientific Publishing Company.
Citation - Scopus: 22
Solitary Wave Solution for a Generalized Hirota-Satsuma Coupled Kdv and Mkdv Equations: a Semi-Analytical Approach
(Elsevier B.V., 2020) Chakraverty, S.; Baleanu, D.; Jena, R.M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. © 2020 Faculty of Engineering, Alexandria University