Results 1 to 10 of about 101 (75)
Numerical Analysis for the Fractional Ambartsumian Equation via the Homotopy Herturbation Method [PDF]
Mathematics, 2020 The fractional calculus is useful in describing the natural phenomena with memory effect. This paper addresses the fractional form of Ambartsumian equation with a delay parameter. It may be a challenge to obtain accurate approximate solution of such kinds of fractional delay equations.
Weam G Alharbi +2 more
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Solution of Ambartsumian Delay Differential Equation with Conformable Derivative [PDF]
Mathematics, 2019 This paper addresses the modelling of Ambartsumian equation using the conformable derivative as an application of the theory of surface brightness in astronomy. The homotopy perturbationmethod is applied to solve this model, where the approximate solution is given in terms of the conformable derivative order and the exponential functions.
Essam R El-Zahar +2 more
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Exact Solution of Ambartsumian Delay Differential Equation and Comparison with Daftardar-Gejji and Jafari Approximate Method [PDF]
Mathematics, 2018 The Ambartsumian equation, a linear differential equation involving a proportional delay term, is used in the theory of surface brightness in the Milky Way. In this paper, the Laplace-transform was first applied to this equation, and then the decomposition method was implemented to establish a closed-form solution.
Abdelhalim Ebaid +2 more
exaly +5 more sources
Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method [PDF]
Mathematical and Computational Applications, 2019 The Ambartsumian delay equation is used in the theory of surface brightness in the Milky way. The Adomian decomposition method (ADM) is applied in this paper to solve this equation. Two canonical forms are implemented to obtain two types of the approximate solutions.
Abdelhalim Ebaid +2 more
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On Analytical Solution of Ambartsumian Equation
The National Academy of Sciences, India, 2017 The Ambartsumian equation is used in the theory of surface brightness in milky way. This equation is a linear differential equation involving a proportional delay term. In this paper we use the Daftardar-Gejji and Jafari method to obtain analytical solution of Ambartsumian equation.
Jayvant Patade +2 more
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A numerical treatment of the delayed Ambartsumian equation over large interval
Journal of Interdisciplinary Mathematics, 2020 In this paper, a numerical technique based on matrix collocation method is presented for approximating the solution of the Ambartsumian equation in terms of the shifted Bernoulli polynomials.
Waleed Adel +2 more
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A Simple Solution for the General Fractional Ambartsumian Equation [PDF]
Applied Sciences, 2022 Fractionalisation and solution of the Ambartsumian equation is considered. The general approach to fractional calculus suitable for applications in physics and engineering is described. It is shown that Liouville-type derivatives are the necessary ones, because they fully preserve backward compatibility with classical results. Such derivatives are used
Manuel Ortigueira, Gabriel Bengochea
openaire +3 more sources
A novel exact solution for the fractional Ambartsumian equation [PDF]
Advances in Difference Equations, 2021 AbstractFractional calculus (FC) is useful in studying physical phenomena with memory effect. In this paper, a fractional form of Ambartsumian equation is considered utilizing the Caputo fractional derivative. The Heaviside expansion formula in classical calculus (CC) is extended/developed in view of FC.
Abdelhalim Ebaid +2 more
exaly +3 more sources
Balancing Accuracy, Efficiency, and Flexibility in Radiation Calculations for Dynamical Models. [PDF]
J Adv Model Earth Syst, 2019 Abstract This paper describes the initial implementation of a new toolbox that seeks to balance accuracy, efficiency, and flexibility in radiation calculations for dynamical models. The toolbox consists of two related code bases: Radiative Transfer for Energetics (RTE), which computes fluxes given a radiative transfer problem defined in terms of ...
Pincus R, Mlawer EJ, Delamere JS.
europepmc +2 more sources
Mathematics, 2021 The fractional generalization of the Ambartsumian delay equation with Caputo’s fractional derivative is considered. The Ambartsumian delay equation is very difficult to be solved neither in the case of ordinary derivatives nor in the case of fractional ...
Weam G Alharbi +2 more
exaly +2 more sources