Article
Multidisciplinary Sciences
Belal Batiha
Summary: In this article, the Daftardar-Gejji and Jafari method (DJM) is utilized to approximate an analytical solution for the sine-Gordon equation. By solving examples, the accuracy of DJM is demonstrated, and a comparison study between DJM, the variational iteration method (VIM), and the exact solution is presented. The comparison of the symmetrical results from this study with existing literature is satisfactory.
Article
Mathematics, Interdisciplinary Applications
Gul Sana, Pshtiwan Othman Mohammed, Dong Yun Shin, Muhmmad Aslam Noor, Mohammad Salem Oudat
Summary: The paper explores the concept of quantum calculus, proposing new q-iterative methods for solving equations and demonstrating their convergence and accuracy through numerical examples. It also establishes an analogy between classical methods and the newly proposed q-iterative methods.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Applied
Gul Sana, Muhmmad Aslam Noor, Dumitru Baleanu
Summary: Quantum calculus, focusing on q-symmetrical outcomes free from limits, rationalizes differentiation and integration operations logically. The paper analyzes its application in iterative methods for solving nonlinear equations, introducing q-iterative methods and investigating their convergence order. The approximate solutions obtained show comparable performance with classical calculus as the quantum parameter q approaches one.
Article
Engineering, Multidisciplinary
Rashid Nawaz, Nasir Ali, Laiq Zada, Kottakkkaran Sooppy Nisar, M. R. Alharthi, Wasim Jamshed
Summary: This article introduces a new method known as the Natural Transform Iterative Method (NTIM) for solving fractional order differential equations, and compares its efficiency and consistency with the existing Natural Transform Decomposition Method (NTDM) using test examples. The results suggest that NTIM is more efficient and consistent than NTDM.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Aziz Khan, Muhammad Imran Liaqat, Manara A. Alqudah, Thabet Abdeljawad
Summary: The aim of this study is to introduce a new computational method, the natural conformable Daftardar-Jafari method (CNDJM), for extracting approximate and exact solutions of the temporal-fractional Swift-Hohenberg (S-H) equations using the conformable natural transform (CNT) and Daftardar-Jafari method (DJM). The efficiency and consistency of the proposed method are assessed by evaluating three types of errors. 2D and 3D graphics are utilized to compare the exact and approximate solutions. This method offers advantages over homotopy analysis and Adomian decomposition methods as it does not require Adomian and He's polynomials, significantly reducing computational work.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Engineering, Mechanical
Manoj Kumar
Summary: In this paper, the Daftardar-Gejji and Jafari method is proposed along with its error analysis for solving systems of nonlinear time-space fractional partial differential equations (PDEs). A variety of nontrivial time-space fractional systems of PDEs are solved, and the obtained solutions occur in either exact form or converging series to a closed form. This method eliminates the need for linearization and discretization, and can be easily implemented using computer algebra systems such as Mathematica, Maple, etc.
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
(2023)
Article
Computer Science, Interdisciplinary Applications
R. A. Talarposhti, Mohsen Alipour, S. E. Ghasemi
Summary: In this study, a well-known fractional nonlinear differential equation, the Zakharov-Kuznetsov equation, is investigated. The Daftardar-Jafari Method (DJM) and He's fractional derivative are used for modeling and obtaining a high precision analytical solution. The results are compared with exact solutions, demonstrating the efficiency and ease of use of DJM. Three-dimensional contour plots are also presented based on suitable parameter values.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
(2022)
Article
Mathematics
Weam Alharbi, Snezhana Hristova
Summary: This paper considers the fractional generalization of the Ambartsumian delay equation with Caputo's fractional derivative, which is difficult to solve using ordinary or fractional derivatives. By combining Laplace transform with Adomian decomposition method, the exact solution is obtained as a series expressed by the Mittag-Leffler functions. The advantage of this approach over existing methods in the literature is discussed.
Article
Computer Science, Hardware & Architecture
Ali Khalouta
Summary: This paper presents a new numerical scheme, called New Decomposition Transform Method (NDTM), for solving nonlinear fractional differential equations. The uniqueness theorem of the solution is established using Banach's fixed point theorem. The convergence analysis and numerical examples demonstrate the effectiveness of the proposed method in analyzing complex fractional problems in various fields of science and engineering.
JOURNAL OF SUPERCOMPUTING
(2023)
Article
Astronomy & Astrophysics
K. Boshkayev, T. Konysbayev, E. Kurmanov, O. Luongo, D. Malafarina, K. Mutalipova, G. Zhumakhanova
Summary: The researchers consider the possibility of the Milky Way's dark matter halo having a non-zero equation of state and evaluate the contributions from the speed of sound produced by the dark matter behaving like a fluid with pressure. Different profiles, including exponential sphere, Einasto, Burkert, and Isothermal, were compared to model the distribution of dark matter in the galactic core. They also investigated the expected experimental signature of gravitational lensing due to the presence of dark matter in the core, showing that current observations cannot distinguish certain scenarios.
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
(2021)
Article
Astronomy & Astrophysics
S. Mau, E. O. Nadler, R. H. Wechsler, A. Drlica-Wagner, K. Bechtol, G. Green, D. Huterer, T. S. Li, Y-Y Mao, C. E. Martinez-Vazquez, M. McNanna, B. Mutlu-Pakdil, A. B. Pace, A. Peter, A. H. Riley, L. Strigari, M-Y Wang, M. Aguena, S. Allam, J. Annis, D. Bacon, E. Bertin, S. Bocquet, D. Brooks, D. L. Burke, A. Carnero Rosell, M. Carrasco Kind, J. Carretero, M. Costanzi, M. Crocce, M. E. S. Pereira, T. M. Davis, J. De Vicente, S. Desai, P. Doel, I Ferrero, B. Flaugher, J. Frieman, J. Garcia-Bellido, M. Gatti, G. Giannini, D. Gruen, R. A. Gruendl, J. Gschwend, G. Gutierrez, S. R. Hinton, D. L. Hollowood, K. Honscheid, D. J. James, K. Kuehn, O. Lahav, M. A. G. Maia, J. L. Marshall, R. Miquel, J. J. Mohr, R. Morgan, R. L. C. Ogando, F. Paz-Chinchon, A. Pieres, M. Rodriguez-Monroy, E. Sanchez, V Scarpine, S. Serrano, I Sevilla-Noarbe, E. Suchyta, G. Tarle, C. To, D. L. Tucker, J. Weller
Summary: We used the latest census data of satellite galaxies in the Milky Way to study the lifetime of particle dark matter (DM). By considering two-body decaying dark matter (DDM), we found that the decay of heavy DM particles significantly depletes the DM content of low-mass subhalos, making them more susceptible to tidal disruption. Using high-resolution simulations and comparing to observations, we excluded certain DDM models and provided strong constraints on the DM particle lifetime.
ASTROPHYSICAL JOURNAL
(2022)
Article
Astronomy & Astrophysics
Andrew P. Cooper, Sergey E. Koposov, Carlos Allende Prieto, Christopher J. Manser, Namitha Kizhuprakkat, Adam D. Myers, Arjun Dey, Boris T. Gansicke, Ting S. Li, Constance Rockosi, Monica Valluri, Joan Najita, Alis Deason, Anand Raichoor, M. -Y. Wang, Y. -S. Ting, Bokyoung Kim, Andreia Carrillo, Wenting Wang, Leandro Beraldo e Silva, Jiwon Jesse Han, Jiani Ding, Miguel Sanchez-Conde, Jessica N. Aguilar, Steven Ahlen, Stephen Bailey, Vasily Belokurov, David Brooks, Katia Cunha, Kyle Dawson, Axel de la Macorra, Peter Doel, Daniel J. Eisenstein, Parker Fagrelius, Kevin Fanning, Andreu Font-Ribera, Jaime E. Forero-Romero, Enrique Gaztanaga, Satya Gontcho A. Gontcho, Julien Guy, Klaus Honscheid, Robert Kehoe, Theodore Kisner, Anthony Kremin, Martin Landriau, Michael E. Levi, Paul Martini, Aaron M. Meisner, Ramon Miquel, John Moustakas, Jundan J. D. Nie, Nathalie Palanque-Delabrouille, Will J. Percival, Claire Poppett, Francisco Prada, Nabeel Rehemtulla, Edward Schlafly, David Schlegel, Michael Schubnell, Ray M. Sharples, Gregory Tarle, Risa H. Wechsler, David H. Weinberg, Zhimin Zhou, Hu Zou
Summary: We describe the Milky Way Survey (MWS), which will be conducted with the Dark Energy Spectroscopic Instrument (DESI), aiming to observe approximately seven million stars and investigate the Galactic structure and stellar evolution. The MWS target selection scheme focuses on the thick disk and stellar halo, including rare stellar types such as white dwarfs, low-mass stars near the Sun, and horizontal branch stars. Our pipelines for deriving radial velocities, atmospheric parameters, and chemical abundances are validated using the DESI Survey Validation program (SV) data, showing good agreement with expectations from mock catalogs and previous surveys.
ASTROPHYSICAL JOURNAL
(2023)
Article
Astronomy & Astrophysics
Hans-Walter Rix, Vedant Chandra, Rene Andrae, Adrian M. Price-Whelan, David H. Weinberg, Charlie Conroy, Morgan Fouesneau, David W. Hogg, Francesca De Angeli, Rohan P. Naidu, Maosheng Xiang, Daniela Ruz-Mieres
Summary: Using data from the Gaia Data Release 3, we have constructed a sample of 2 million bright giant stars, revealing an ancient and metal-poor population in the Milky Way. These stars have a spatial distribution concentrated around the Galactic center, with most orbits confined to the inner Galaxy. They likely predate the oldest disk population, implying they formed in the early stages of the Milky Way.
ASTROPHYSICAL JOURNAL
(2022)
Article
Astronomy & Astrophysics
Anna-Christina Eilers, David W. Hogg, Hans-Walter Rix, Melissa K. Ness, Adrian M. Price-Whelan, Szabolcs Meszaros, Christian Nitschelm
Summary: In order to understand the formation of the Milky Way's prominent bar, it is necessary to study whether the stars in the bar have different chemical element compositions compared to the stars in the disk. A new self-calibration approach is developed in this study to eliminate modeling and astrophysical abundance systematics among red giant branch (RGB) stars. The results indicate that there are no abundance variations that match the geometry of the bar and that the mean abundance gradients vary smoothly and monotonically with galactocentric radius.
ASTROPHYSICAL JOURNAL
(2022)
Article
Mathematics
Ioannis K. Argyros, Samundra Regmi, Stepan Shakhno, Halyna Yarmola
Summary: This article updates the convergence developments of Newton's method for solving nonlinear equations. It introduces a finer theory to replace the Kantorovich theory, requiring weaker conditions. The article also proves the convergence order is two under these conditions, and the new convergence ratio is at least as small. Numerical experiments are conducted to complement the study.
Article
Mathematics, Applied
Sachin Bhalekar, Madhuri Patil
Article
Physics, Multidisciplinary
Sachin Bhalekar
PRAMANA-JOURNAL OF PHYSICS
(2019)
Article
Mathematics, Applied
Sachin Bhalekar, Madhuri Patil
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2019)
Article
Physics, Multidisciplinary
Madhuri Patil, Sachin Bhalekar
PRAMANA-JOURNAL OF PHYSICS
(2020)
Article
Engineering, Mechanical
Sachin Bhalekar, Madhuri Patil
NONLINEAR DYNAMICS
(2020)
Article
Mathematics, Interdisciplinary Applications
Prashant M. Gade, Sachin Bhalekar
Summary: This study investigates the stability of linear fractional order maps and finds that the evolution in the stable region is described by Mittag-Leffler functions with a well-defined effective Lyapunov exponent. The research also explores coupled linear fractional maps and stability at fixed points of fractional nonlinear maps, providing insights into the relationship between stability and eigenvalues of coefficient matrices.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics, Interdisciplinary Applications
Sachin Bhalekar, Prashant M. Gade, Divya Joshi
Summary: This article extends the definition of n-dimensional difference equations to complex order and investigates the stability of linear systems defined by an n-dimensional matrix. It derives the conditions for the stability of the zero solution of linear systems. For the one-dimensional case, it finds that the stability region, if any, is enclosed by a boundary curve and obtains a parametric equation for it. Furthermore, it observes that there is no stable region if this parametric curve is self-intersecting. The article also highlights that even for real eigenvalues, the solutions can be complex, and the dynamics in one dimension are richer than the case for real order. These findings can be extended to n-dimensions. For nonlinear systems, it concludes that the stability of the linearized system determines the stability of the equilibrium point.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Sumit S. Pakhare, Sachin Bhalekar, Prashant M. Gade
Summary: Coupled differential equations and coupled maps are widely used in science and engineering. This study investigates the coupling between integer order systems and fractional order systems, and reveals the dependence of stability on the stability of the fractional system, providing stability criteria.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Divya D. Joshi, Prashant M. Gade, Sachin Bhalekar
Summary: In this study, we investigate the fractional maps of complex order in one and two dimensions and find that smooth maps tend to exhibit regular behavior while discontinuous or non-differentiable maps may show chaos. Additionally, complex fractional-order maps that exhibit chaos in two dimensions also demonstrate multistability.
Article
Mathematics, Interdisciplinary Applications
Sachin Bhalekar, Deepa Gupta
Summary: This study focuses on the stability analysis of a fractional order delay differential equation and provides linearized stability conditions. The stable region sketch in the q delta-plane is provided for any positive epsilon and p. Additionally, chaos in the proposed model is investigated for a wide range of delay parameter.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Sachin Bhalekar, Prashant M. Gade
Summary: This study investigates the stability of synchronized fixed-point state for linear fractional-order coupled map lattice (CML). It is observed that the eigenvalues of the connectivity matrix determine the system's stability, similar to that in integer-order CML. Exact bounds are found for a one-dimensional lattice with translationally invariant coupling using the theory of circulant matrices, which can be extended to any finite dimension. Similar analysis can be conducted for the synchronized fixed point of nonlinear coupled fractional maps, where eigenvalues of the Jacobian matrix play the same role. The analysis demonstrates that the eigenvalues of the connectivity matrix play a pivotal role in the stability analysis of synchronized fixed point even in coupled fractional maps.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
M. Priyanka, P. Muthukumar, Sachin Bhalekar
Summary: Investigated a two-species prey-predator system with immigration and harvesting factors, finding potential diversity in population dynamics. The findings were validated through theoretical analysis and numerical simulations.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Mathematics, Interdisciplinary Applications
Divya D. Joshi, Sachin Bhalekar, Prashant M. Gade
Summary: This work investigates the stability of fractional-order linear difference equations under feedback, finding that stability is related to the feedback time z. The cases of z=1 and z=2 are studied in further detail, and the stability of fixed points under feedback for nonlinear fractional order difference equations with fixed points x*=0 is also examined.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Aline Hosry, Roger Nakad, Sachin Bhalekar
MATHEMATICAL AND COMPUTATIONAL APPLICATIONS
(2020)
Correction
Multidisciplinary Sciences
Jayvant Patade, Sachin Bhalekar
PHYSICAL SCIENCES REVIEWS
(2018)
