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
doaj +4 more sources
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
doaj +4 more sources
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
doaj +4 more sources
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
doaj +4 more sources
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
doaj +4 more sources
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
doaj +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.
Abdelhalim Ebaid +3 more
doaj +4 more sources
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
doaj +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 Alharbi, Snezhana Hristova
doaj +3 more sources
A study of fractional order Ambartsumian equation involving exponential decay kernel
AIMS Mathematics, 2021 Récemment, les opérateurs fractionnaires non singuliers ont un rôle important dans la modélisation des problèmes du monde réel. Plus précisément, les opérateurs Caputo-Fabrizio sont utilisés pour étudier une meilleure dynamique des processus de mémoire.
Shabir Ahmad +3 more
openaire +5 more sources