Modified Laplace transform and its properties

Saif, Mohd; Khan, Faisal; Nisar, Kottakkaran Sooppy; Aracı, Serkan

doi:10.22436/jmcs.021.02.04

Cited by 13 publications

(20 citation statements)

References 8 publications

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“…In our present investigation, by using the idea given in reference [1], we have introduced some modified forms for basic extended special functions such as Gamma function, Beta function, hypergeometric function and confluent hypergeometric function. We have investigated some properties of these functions.…”

Section: Resultsmentioning

confidence: 99%

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Certain investigations in the field of special functions

Kulib¹,

Al-Gonah²,

Barahmah³

2020

J. Math. Anal. Model.

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Motivated mainly by a variety of applications of Euler's Beta, hypergeometric, and confluent hypergeometric functions together with their extensions in a wide range of research fields such asengineering, chemical, and physical problems. In this paper, we introduce modified forms of some extended special functions such as Gamma function, Beta function, hypergeometric function and confluent hypergeometric function by making use of the idea given in reference \cite{9}. Also, certain investigations including summation formulas, integral representations and Mellin transform of these modified functions are derived. Further, many known results are obtained asspecial cases of our main results.

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Section: Resultsmentioning

confidence: 99%

“…Motivated by the idea given in [1], in this paper, we introduce a new modified forms of the extended Gamma, Beta, hypergeometric and confluent hypergeometric functions defined in equations (1.4)-(1.7) respectively.…”

Section: Introductionmentioning

confidence: 99%

Certain investigations in the field of special functions

Kulib¹,

Al-Gonah²,

Barahmah³

2020

J. Math. Anal. Model.

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“…To get their hands on these complex behaviors, several researchers invest themselves in the development of approximate solutions and others in numerical and/or experimental analysis. As an example we can cite the recent works [37] where, is found the solutions of the fractional kinetic equation related with the (p, q)-Mathieu-type series through the procedure of Sumudu and Laplace transforms, [35] that a modified Laplace transform and its properties are analyzed, [3] where a novel approach termed as fractional iteration algorithm-I for finding the numerical solution of nonlinear noninteger order partial differential equations is presented. Another example is a new analyzing tool, called the fractional iteration algorithm I for finding numerical solutions of nonlinear time fractional-order Cauchy reaction-diffusion model equations proposed in [4].…”

Section: Introductionmentioning

confidence: 99%

Chaos control and synchronization of a new chaotic financial system with integer and fractional order

Dousseh¹,

Ainamon²,

Miwadinou³

et al. 2021

J. Nonlinear Sci. Appl.

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Synchronization of chaotic dynamical systems with fractional order is receiving great attention in recent literature because of its applications in a variety of fields including optics, secure communications of analog and digital signals, and cryptographic systems. In this paper, chaos control of a new financial system, and chaos synchronization between two identical financial systems, and non-identical financial systems with integer and fractional order are investigated. Chaos control is based on a linear feedback controller for stabilizing chaos to unstable equilibrium. In addition, chaos synchronization, not only between two identical new chaotic financial systems, but also between the new financial system and an another financial system given in the literature is realized by using active control technique. The synchronization is done for integer and fractional order in each case. It is shown that chaotic behavior can be controlled easily to any unstable equilibrium point of the new financial system. Also, it is observed that synchronization is enhanced when the fractional order increases and approximates to one. Numerical simulations are used to verify the proposed methods.

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“…Integral transforms have been played a key role to solve the differential or integrodifferential equations cf. [1][2][3][4][5][6][7][8][9][10][11][12]. One of the most useful integral transforms is the Laplace transform, for f being a function defined for 0 t  , defined by…”

Section: Introductionmentioning

confidence: 99%

Modified Sumudu Transform and Its Properties

Duran

2021

Sakarya University Journal of Science

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Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, hyperbolic sine, hyperbolic cosine, exponential function, and function derivatives. Moreover, we attain two shifting properties and a scale preserving theorem for the modified Sumudu transform. We give modified inverse Sumudu transform and investigate some relations and examples. Furthermore, we show that the modified Sumudu transform is the theoretical dual transform to the modified Laplace transform.

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Modified Laplace transform and its properties

Cited by 13 publications

References 8 publications

Certain investigations in the field of special functions

Certain investigations in the field of special functions

Chaos control and synchronization of a new chaotic financial system with integer and fractional order

Modified Sumudu Transform and Its Properties

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