Article
Mathematics, Applied
Qinxu Ding, Patricia J. Y. Wong
Summary: This paper develops a higher order numerical method for the fractional Bagley-Torvik equation, utilizing a new fourth-order approximation for the fractional derivative and a discrete cubic spline approach. The theoretical convergence order of the method is shown to improve upon previous work. Five examples are provided to demonstrate the efficiency of the method and compare it with others in the literature.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Hazrat Ali, Md. Kamrujjaman, Afroza Shirin
Summary: In this paper, a new numerical solution scheme for the Bagley-Torvik equation of order (0, 2) based on the finite element method is developed, showing its accuracy, efficiency, and simplicity through numerical examples and results. The method's accuracy is better than existing methods, providing guidance for solving fractional-order boundary value problems.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2021)
Article
Mathematics, Interdisciplinary Applications
Mohamed Fathy, K. M. Abdelgaber
Summary: This paper presents and applies the Galerkin method to obtain semi-analytical solutions of quadratic Riccati and Bagley-Torvik differential equations in fractional order. New theorems are proposed to optimize the efficiency of the method by minimizing the generated residual. The proposed method is compared with other methods through solving initial value problems of different fractional orders, and the results are illustrated using tables and figures. The Legendre-Galerkin method is found to be efficient and reliable for these problems.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Multidisciplinary
Lei Shi, Soumia Tayebi, Omar Abu Arqub, M. S. Osman, Praveen Agarwal, W. Mahamoud, Mahmoud Abdel-Aty, Mohammed Alhodaly
Summary: In this analysis, the high order cubic B-spline method is used to approximate solutions for fractional Painleve' and Bagley-Torvik equations. The approach considers different boundary set conditions. The discretization of the fractional model problems is achieved using a piecewise spline of a 3rd-degree polynomial. The spline method is demonstrated to be cost-efficient and precise in its calculations, making it suitable for various applications.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Materials Science, Multidisciplinary
Kamran, Muhammad Asif, Kamal Shah, Bahaaeldin Abdalla, Thabet Abdeljawad
Summary: This article aims to solve the Bagley-Torvik equation involving the Atangana-Baleanu derivative using the Laplace transform method. The Laplace transform is an effective tool for solving differential equations, but sometimes leads to solutions in the Laplace domain that cannot be inverted back to the time domain analytically. Therefore, numerical methods are used to convert the solution from the Laplace domain to the time domain. Four numerical inverse Laplace transform methods are utilized, and their accuracy and efficiency are validated through four test problems. The computational results are presented using tables and figures, and compared with other methods in the literature to demonstrate the superiority of the proposed methods.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Applied
Murugesan Meganathan, Thabet Abdeljawad, M. Motawi Khashan, Gnanaprakasam Britto Antony Xavier, Fahd Jarad
Summary: This research introduces a discrete version of the fractional Bagley-Torvik equation and obtains solutions using the nabla discrete Laplace transform. The solutions are expressed in terms of Mittag-Leffler functions with three parameters and are numerically handled for specific examples.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Applied
Tianyi Pu, Marco Fasondini
Summary: We propose a spectral method for one-sided linear fractional integral equations on a closed interval, achieving exponential convergence even for equations with irrational or multiple fractional orders. The method utilizes Jacobi fractional polynomials, a new orthogonal basis obtained from weighted classical Jacobi polynomials. We introduce new algorithms for constructing the matrices used to represent fractional integration operators. Despite the instability and high-precision computations required, the spectral method produces well-conditioned and efficient linear systems. In comparison to a sparse spectral method, our orthogonal basis-based method demonstrates superior stability for time-fractional heat and wave equations.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Ahmed Z. Amin, Mohamed A. Abdelkawy, Emad Solouma, Ibrahim Al-Dayel
Summary: This paper proposes a numerical solution based on the shifted Legendre Gauss-Lobatto collocation technique for the non-linear distributed-order fractional Bagley-Torvik differential equation, and verifies its accuracy through numerical examples.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Haiyong Xu, Lihong Zhang, Guotao Wang
Summary: This paper investigates the existence of extremal solutions for a nonlinear boundary value problem involving the Caputo-Fabrizio-type fractional differential operator. By utilizing a new inequality and applying a monotone iterative technique with upper and lower solutions, the main result is obtained. The paper concludes with an illustrative example.
FRACTAL AND FRACTIONAL
(2022)
Article
Engineering, Multidisciplinary
Ahmed Z. Amin, Antonio M. Lopes, Ishak Hashim
Summary: A numerical approach based on the shifted Chebyshev-Gauss collocation method is proposed to solve the nonlinear variable-order fractional Bagley-Torvik differential equation (VO-FBTE). The solution of the VO-FBTE is approximated using a truncated series of shifted Chebyshev polynomials, with the interpolation nodes chosen as the shifted fractional Chebyshev-Gauss collocation points. The accuracy of the proposed method is confirmed through numerical examples and compared against other methods.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Engineering, Multidisciplinary
Suayip Yuzbasi, Gamze Yildirim
Summary: In this study, a collocation approach is proposed to solve the Bagley-Torvik equation, a type of fractional differential equation. The method utilizes Laguerre polynomials and matrix relations to convert the problem into a system of linear algebraic equations, leading to approximate solutions. Additionally, an error estimation method is provided, and the Laguerre polynomial solution is improved for enhanced accuracy.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Multidisciplinary Sciences
Diego Caratelli, Pierpaolo Natalini, Paolo Emilio Ricci, Dongfang Li, Junesang Choi
Summary: This paper approximates the solution of a generalized form of the Bagley-Torvik equation using Taylor's expansions in fractional powers, and verifies the findings by studying the fractional Laguerre-type logistic equation.
Article
Multidisciplinary Sciences
Saeed Althubiti, Abdelaziz Mennouni
Summary: This study proposes an effective method for approximating solutions to the Bagley-Torvik system and obtains interesting original results.
Article
Mathematics, Applied
Hossein Fazli, Hongguang Sun, Sima Aghchi, Juan J. Nieto
Summary: In this study, the existence of extremal solutions for a class of fractional differential equations in fluid dynamics was investigated. By establishing a new comparison theorem and applying the classical monotone iterative approach, sufficient conditions for the existence of extremal solutions were established and twin convergent monotone explicit iterative schemes were constructed. Special cases of the discussed problem include the generalized nonlinear nonlocal Bagley-Torvik equation and the generalized Basset equation with nonlinear source functions.
CARPATHIAN JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Laique Zada, Imran Aziz
Summary: Haar wavelet collocation technique is used to obtain approximate solutions for fractional KdV, Burgers', and KdV-Burgers' equations, involving discretization and solving of nonlinear fractional differential equations. The proposed method demonstrates accuracy, efficiency, and simplicity in many test problems.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Energy & Fuels
Hari Mohan Srivastava, Ziad Khan, Pshtiwan Othman Mohammed, Eman Al-Sarairah, Muhammad Jawad, Rashid Jan
Summary: The theoretical influence of buoyancy and thermal radiation on magnetohydrodynamic (MHD) flow across a stretchable porous sheet was analyzed in this study. The Darcy-Forchheimer model and laminar flow were used, along with the consideration of temperature-dependent heat source or sink, Brownian motion, and thermophoresis. The results showed a favorable comparison with earlier studies and demonstrated the effects of different physical parameters on velocity, temperature, and concentration fields. This model has important applications in various fields such as steel rolling, nuclear explosions, and solar power technology. The study also provided insights into the behavior of skin friction, Sherwood number, Nusselt number, and other parameters.
Article
Mathematics
Naied A. Nayied, Firdous A. Shah, M. A. Khanday
Summary: This article proposes an efficient Fibonacci wavelet-based collocation method for solving the nonlinear reaction-diffusion equation of Fisher-type. It formulates operational matrices of integration corresponding to the Fibonacci wavelets and conducts error analysis and convergence theorem. The proposed technique demonstrates computational effectiveness and precise outcomes compared to existing methods.
JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Hare Krishna Nigam, Hari Mohan Srivastava, Swagata Nandy
Summary: In this paper, we determine the convergence rate of a function with two-dimensional variables in generalized Holder spaces using matrix means of its conjugate Fourier series. We also investigate the convergence rate of a function with N-dimensional variables in generalized Holder spaces using the same method, and deduce significant corollaries from our main results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
H. M. Srivastava, Sitaram Yadav, S. K. Upadhyay
Summary: This paper investigates the linear partial differential operators and generalized distributions associated with the Fourier transform using convolution properties. It examines various properties of the Weinstein transform on the generalized distributions and other spaces. The convolution properties of the generalized distributions associated with the Weinstein transform on the space D'(?)(Rn+1 (+)) are also discussed.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2023)
Correction
Mathematics
H. M. Srivastava, Sarem H. Hadi, Maslina Darus
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2023)
Article
Mathematics
Ekram E. Ali, Hari M. Srivastava, Abdel Moneim Y. Lashin, Abeer M. Albalahi
Summary: In this article, two new subclasses (aq, q) and (a, q) of meromorphic functions in the open unit disk U are introduced and studied using the q-binomial theorem. These subclasses refer to analytic functions in the punctured unit disk U-* = U \ {0} = {z : z ? C and 0 < |z| < 1}. The inclusion relations are derived and an integral operator that preserves functions in these function classes is investigated. Additionally, a strict inequality involving a newly introduced linear convolution operator is established, and special cases and corollaries of the main results are considered.
Article
Mathematics
Pishtiwan Othman Sabir, Hari Mohan Srivastava, Waggas Galib Atshan, Pshtiwan Othman Mohammed, Nejmeddine Chorfi, Miguel Vivas-Cortez
Summary: This paper presents a new general subfamily N-Sigma m(u,v) (eta,mu,gamma,l) of the family Sigma(m) that contains holomorphic normalized m-fold symmetric bi-univalent functions in the open unit disk D associated with the Ruscheweyh derivative operator. It provides estimates of the Taylor-Maclaurin coefficients |a(m+1)| and |a(2m+1)| for functions belonging to this family, and discusses the consequences of the results. The current findings extend and enhance recent studies in this field, and establish several connections with known results in specific scenarios.
Article
Mathematics
Hari M. Srivastava, Rogayeh Alavi, Saeid Shams, Rasoul Aghalary, Santosh B. Joshi
Summary: In this paper, we modify a famous theorem on the principle of differential subordination to apply to normalized analytic functions with fixed initial Taylor-Maclaurin coefficients. Using this modified form, we generalize and improve several recent results in the literature on the geometric function theory of complex analysis. We also prove simple conditions for starlikeness, convexity, and the strong starlikeness of several one-parameter families of integral operators, including a certain mu-convex integral operator and the familiar Bernardi integral operator.
Article
Mathematics
H. K. Nigam, H. M. Srivastava
Summary: This paper investigates the use of nonlinear diffusion for denoising audio signals by applying it to wavelet coefficients obtained from different filters. The results show a significant improvement in denoising compared to wavelet shrinkage.
Article
Mathematics, Interdisciplinary Applications
Mohammad Izadi, Hari Mohan Srivastava
Summary: This paper proposes two accurate and efficient spectral collocation techniques for handling a nonlinear fractional system in financial modeling with chaotic behavior. The techniques are based on a domain-splitting strategy, where the spectral method is applied locally in each subdomain. The methods use the generalized version of modified Bessel polynomials and a combination of quasilinearization method and direct numerical matrix method. Convergence theorem and error bounds are proved, and simulation results demonstrate the utility and applicability of the proposed techniques.
Article
Mathematics, Interdisciplinary Applications
Seng Huat Ong, Shin Zhu Sim, Shuangzhe Liu, Hari M. Srivastava
Summary: This paper introduces a flexible family of discrete distributions based on a finite mixture model for handling under-, equi- and over-dispersion in count data. The family is exemplified using a mixture of negative binomial and shifted negative binomial distributions, and their properties are derived. Hypothesis testing and simulation studies are performed to analyze the power and parameter estimation methods. The utility of the distributions is illustrated through their application to real biological data sets, showing better fit compared to well-known distributions like the generalized Poisson and COM-Poisson for different levels of dispersion in count data.
Article
Mathematics, Applied
H. M. Srivastava, Shakir Hussain Malik, M. I. Qureshi, Bilal Ahmad Bhat
Summary: This paper aims to establish four general double-series identities involving suitably-bounded sequences of complex numbers using zero-balanced terminating hypergeometric summation theorems and series rearrangement technique. The sum (or difference) of two general double hypergeometric functions of the Kampe 'de Fe' riet type are obtained in terms of a generalized hypergeometric function under appropriate convergence conditions. The paper also derives a closed form for the Clausen hypergeometric function -27z! 3F2 4(1-z)3 and a reduction formula for the Srivastava-Daoust double hypergeometric function with the arguments (z, -z4). Many of the reduction formulas are verified using Mathematica software program, and potential directions for further research are indicated.
Article
Mathematics, Applied
Raksha, H. M. Srivastava, N. V. Sayinath Udupa, B. R. Srivatsa Kumar
Summary: In this article, Shaun Cooper proved interesting 1i-function identities of level 6 while finding series and iterations for 1/pi, and presented new proofs of these identities. The author utilized the modular equation of degree 3 in two methods and provided combinatorial interpretations of colored partitions. The article also discussed the potential direction for further research based on recent developments involving Jacobi's triple-product identity, theta-function identities, and various q-functions.
Article
Mathematics, Interdisciplinary Applications
Hari M. M. Srivastava, Mohammad Izadi
Summary: In this manuscript, the author discusses the numerical solutions of a class of fractional-order differential equations with singularity and strong nonlinearity pertaining to electrohydrodynamic flow in a circular cylindrical conduit. The nonlinearity of the underlying model is removed by the quasilinearization method (QLM), and a family of linearized equations is obtained. Through numerical simulations, it is shown that the proposed hybrid QLM-SAPSK approach is capable of tackling the inherit singularity at the origin and produces effective numerical solutions to the model problem with different nonlinearity parameters and two fractional order derivatives. The accuracy of the present technique is checked via the technique of residual error functions. The QLM-SAPSK technique is simple and efficient for solving the underlying electrohydrodynamic flow model, and the computational outcomes are accurate in comparison with those of numerical values reported in the literature.
FRACTAL AND FRACTIONAL
(2023)
Article
Chemistry, Multidisciplinary
Mohammad Izadi, Hari M. Srivastava
Summary: This paper presents a numerical treatment method for a class of boundary value problems with singularity and nonlinearity. The proposed technique combines spectral matrix technique and quasilinearization method, using a novel class of polynomials introduced by S.K. Chatterjea. The convergence analysis of the method is proven and numerical examples demonstrate its efficiency and flexibility in solving similar problems in science and engineering.
APPLIED SCIENCES-BASEL
(2023)
