Results 1 to 10 of about 1,218,779 (86)
A Simple Solution for the General Fractional Ambartsumian Equation [PDF]
Applied Sciences (Switzerland), 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.
Gabriel Bengochea, Manuel D Ortigueira
exaly +5 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.
Sergei Petrovskii, Weam Alharbi
exaly +5 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.
Abdelhalim Ebaid
exaly +6 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.
Essam El-zahar +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.
Mona D. Aljoufi, Abdelhalim Ebaid
exaly +5 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 ...
Snezhana Hristova, Weam Alharbi
exaly +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.
J F Gómez-Aguilar +2 more
exaly +4 more sources
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.
Essam El-zahar +2 more
exaly +3 more sources
Accurate Solution for the Pantograph Delay Differential Equation via Laplace Transform
Mathematics, 2023 The Pantograph equation is a fundamental mathematical model in the field of delay differential equations. A special case of the Pantograph equation is well known as the Ambartsumian delay equation which has a particular application in Astrophysics.
Reem Alrebdi, Hind K. Al-Jeaid
doaj +2 more sources
International Journal of Analysis and Applications, 2022 In electric trains, the current is collected via a certain device, called the Pantograph. The governing mathematical model of such physical problem is well-known as the Pantograph delay differential equation (PDDE): y’(t)=ay(t)+by(ct), where c is a ...
S. M. Khaled
doaj +1 more source