Introducing the upadhyaya integral transform

Upadhyaya, Lalit Mohan

doi:10.5958/2320-3226.2019.00051.1

Cited by 5 publications

(5 citation statements)

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“…In the general formulation of the Upadhyaya transform, 2 1 ,   and 3  are complex parameters; however, for the sake of this research, we will assume that all of these parameters are positive real numbers (see Upadhyaya [2] and Upadhyaya et al [18]).…”

Section: Nomenclature Of Symbolsmentioning

confidence: 99%

“…These transformations result in very successful solutions in a wide range of industries. The Upadhyaya transform (UT), which is the most significant generalization of virtually all conventional forms of the Laplace transform in mathematics, was developed by Upadhyaya [2]. In order to estimate the blood glucose concentration at the moment of an intravenous injection, Higazy et al [3] established the Sawi decomposition approach and identified the primitive (solution) of Volterra integral equation.…”

Section: Introductionmentioning

confidence: 99%

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Exact Solutions of Cardiovascular Models by using Upadhyaya Transform

Thakur,

Kuffi

2024

Jour. Kufa Math. Comp.

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In many practical fields, such as engineering, physics, chemistry, biology, psychology, economics, and finance, processes are simulated using differential equations. These models solutions, in contrast to algebraic equations, may be more intricate. In order to get at the solutions to these models, it is easy to employ integral transformations. In this paper, we use the Upadhyaya transform to obtain accurate solutions to two cardiovascular models. It is obvious that the Upadhyaya transform is an effective, dependable, and simple technique for solving differential equations.

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Section: Nomenclature Of Symbolsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact Solutions of Cardiovascular Models by using Upadhyaya Transform

Thakur,

Kuffi

2024

Jour. Kufa Math. Comp.

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“…In the recent years, researchers developed numerous new integral transforms (Shehu [33]; Sumudu [34]; Natural [35]; Elzaki [36]; Aboodh [37]; Mahgoub [38]; Kamal [39]; ZZ [40]; Mohand [41]; Sadik [42]; Shehu [43]; Sawi [44]; Upadhyay [45]; Jafari [46]) and used them to handle the problems of Science and Engineering. Higazy et al [47] introduced a new decomposition method "Sawi decomposition method" to determine the solution of Volterra integral equation.…”

Section: Introductionmentioning

confidence: 99%

Solution of Linear Volterra Integral Equation of Second Kind via Rishi Transform

Aggarwal¹,

Kumar

Chandel

2023

J. Sci. Res.

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The solution of various problems of engineering and science can easily determined by representing these problems in integral equations. There are numerous analytical and numerical methods which can be used for solving different kinds of integral equations. In this paper, authors used recently developed integral transform “Rishi Transform” for obtaining the analytical solution of linear Volterra integral equation of second kind (LVIESK). For this, the kernel of LVIESK has assumed a convolution type kernel. Five numerical examples are considered for demonstrating the complete procedure of determining the solution. Results of these problems suggest that Rishi transform provides the exact analytical solution of LVIESK without doing complicated calculation work.

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“…Each of these transformations has unique properties and applications. Also for studies on these transformations, (Watugala [1], Khan and Khan [2], Elzaki [3], Upadhyaya [4], Jafari [5], Luchko et al [6], Jumarie [7], Romero et al [8], Mahor et al [9] and Kumar [10]).…”

Section: Introductionmentioning

confidence: 99%

New generalized Mellin transform and applications to partial and fractional differential equations

Ata

Kıymaz

2023

International Journal of Mathematics and Computer in Engineering

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In this paper, we introduce a generalized Mellin transformation in a general form that encompasses the generalized Mellin transformations found in the literature. Then, we give the fundamental properties of this new integral transformation and apply it to some elementary functions. Furthermore, we obtain the solutions of partial and fractional differential equations by means of this new integral transformation. Finally, we examine the relations between generalized Mellin transformations in the literature and the new generalized Mellin transformation and present a table showing the new integral transformations of functions commonly used in mathematics, physics and engineering applications.

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Introducing the upadhyaya integral transform

Cited by 5 publications

References 0 publications

Exact Solutions of Cardiovascular Models by using Upadhyaya Transform

Exact Solutions of Cardiovascular Models by using Upadhyaya Transform

Solution of Linear Volterra Integral Equation of Second Kind via Rishi Transform

New generalized Mellin transform and applications to partial and fractional differential equations

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