A novel exact solution for the fractional Ambartsumian equation [PDF]
Advances in Difference Equations, 2021 Fractional 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.
Abdelhalim Ebaid +3 more
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Iterative methods of Ambartsumian equations’ solutions. Part 2
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2022 Background. Ambartsumian equation and its generalizations are one of the main integral equations of astrophysics, which have found wide application in many areas of physics and technology.
I.V. Boykov, A.A. Pivkina
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A Simple Solution for the General Fractional Ambartsumian Equation
Applied Sciences, 2023 Fractionalisation and solution of the Ambartsumian equation is considered. The general approach to fractional calculus suitable for applications in physics and engineering is described.
Manuel Duarte Ortigueira +1 more
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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.
Weam Alharbi, Sergei Petrovskii
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The Riemann–Liouville fractional derivative for Ambartsumian equation
Results in Physics, 2020 The Ambartsumian equation, based on the modified Riemann–Liouville fractional derivative, is analyzed in this paper. The solution is expressed as a power series of arbitrary powers and its convergence has been proven.
E.R. El-Zahar +4 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.
Sayed M. Khaled +2 more
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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.
Abdelhalim Ebaid +3 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.
Huda O. Bakodah, Abdelhalim Ebaid
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Solution of Ambartsumian Delay Differential Equation in the q-Calculus
International Journal of Analysis and Applications, 2020 The Ambartsumian equation in view of the q-calculus is investigated in this paper. This equation is of practical interest in the theory of surface brightness in the Milky Way. Two approaches are applied to obtain the closed form solution.
Abdulaziz M. Alanazi, Abdelhalim Ebaid
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Iterative methods for solving Ambartsumian’s equations. Part 1
University proceedings. Volga region. Physical and mathematical sciences, 2021 Background. Ambartsumian’s equation and its generalizations are one of the main integral equations of astrophysics, which have found wide application in many areas of physics and technology. An analytical solution to this equation is currently unknown, and the development of approximate methods is urgent.
I.V. Boykov, A.A. Shaldaeva
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