Analytic solutions of fractional differential equation associated with RLC electrical circuit

Gill, Vinod; Modi, Kanak; Singh, Yuvraj

doi:10.1080/09720510.2018.1466966

Cited by 27 publications

(17 citation statements)

References 4 publications

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“…The exact solution of the model under investigation is obtained in terms of the Fox H-function with the help of the Sumudu integral transform. The motivation behind the present investigation comes from published research work [22] wherein authors have used the Sumudu integral transform to find an exact solution for the RLC linear circuit model under the Caputo differential operator, however, they have expressed their computed solution in terms of the Mittag-Leffler function.…”

Section: Introductionmentioning

confidence: 99%

Fox H-functions as exact solutions for Caputo type mass spring damper system under Sumudu transform

Qureshi¹

2021

J. Appl. Math. Comput. Mech.

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Closed form solutions for mathematical systems are not easy to find in many cases. In particular, linear systems such as the population growth/decay model, RLC circuit, mixing problems in chemistry, first-order kinetic reactions, and mass spring damper system in mechanical and mechatronic engineering can be handled with tools available in theoretical study of linear systems. One such linear system has been investigated in the present research study. The second order linear ordinary differential equation called the mass spring damper system is explored under the Caputo type differential operator while using the Sumudu integral transform. The closed form solution has been found in terms of the Fox H-function wherein different aspects of the solution can be obtained with variation in α ∈ (1, 2] and β ∈ (0, 1]. The classical mass spring damper model is retrieved for α = β = 1.

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Section: Introductionmentioning

confidence: 99%

Fox H-functions as exact solutions for Caputo type mass spring damper system under Sumudu transform

Qureshi¹

2021

J. Appl. Math. Comput. Mech.

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“…Fractional differential equations are vitally important due to their proved and diverse uses in engineering and every part of science. Due to frequent appearance of fractional differential equations in different disciplines of engineering and science, the researchers have added a lot of research contribution to both theory of mathematical science and technology [1][2][3][4][5]. Fractional differential equations are the best for modeling of various processes in engineering and physical sciences.…”

Section: Introductionmentioning

confidence: 99%

A Reliable Computational Algorithm for Solving Fractional Biological Population Model

Devi

Jakhar

2021

J. Sci. Res.

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In this work, authors obtained the series solution of nonlinear fractional partial differential equations, which is emerging in a spatial diffusion of biological population model using Elzaki transform homotopy perturbation method (ETHPM). The Elzaki transform homotopy perturbation method is a combined form of the Elzaki transform and homotopy perturbation method. Three test illustrations are used to show the proficiency and accuracy of the projected method. It has been observed that the proposed technique can be widely employed to examine other real world problems. The results obtained with the help of the proposed technique are plotted for different fractional orders.

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“…In the last decade, considerable interest in fractional differential equations has been stimulated due to their numerous applications in the areas of physics, biology, engineering, and other areas. Several numerical and analytical methods have been developed to study the solutions of nonlinear fractional partial differential equations, for details, refer to the work in [1][2][3][4][5][6]. Fractional equations have enabled the investigation of the nonlocal response of multiple phenomena such as diffusion processes, electrodynamics, fluid flow, elasticity, and many more.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Generalized Space-Time Fractional Advection-Dispersion Equation via Coupling of Sumudu and Fourier Transforms

Gill¹,

Singh

2019

Front. Phys.

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The objective of this article is to present the computable solution of space-time advection-dispersion equation of fractional order associated with Hilfer-Prabhakar fractional derivative operator as well as fractional Laplace operator. The method followed in deriving the solution is that of joint Sumudu and Fourier transforms. The solution is derived in compact and graceful forms in terms of the generalized Mittag-Leffler function, which is suitable for numerical computation. Some illustration and special cases of main theorem are also discussed.

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Analytic solutions of fractional differential equation associated with RLC electrical circuit

Cited by 27 publications

References 4 publications

Fox H-functions as exact solutions for Caputo type mass spring damper system under Sumudu transform

Fox H-functions as exact solutions for Caputo type mass spring damper system under Sumudu transform

A Reliable Computational Algorithm for Solving Fractional Biological Population Model

Analytical Solution of Generalized Space-Time Fractional Advection-Dispersion Equation via Coupling of Sumudu and Fourier Transforms

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