Alpha fractional frequency Laplace transform through multiseries

Meganathan, M.; Abdeljawad, Thabet; Gnanaprakasam, Britto Antony Xavier; Jarad, Fahd

doi:10.1186/s13662-020-02691-0

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2022

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“…Recently, Bastos et al developed the theory on h-sum and h-di erence operators in discrete fractional calculus. For more recent applications of fractional Laplace transform, one can refer [8][9][10][11]. ese concepts are very well applied in discrete fractional transforms in the field of fractional calculus [12].…”

Section: Introductionmentioning

confidence: 99%

The Generalized Fractional Proportional Delta Operator and New Generalized Transforms in Discrete Fractional Calculus

Amalraj¹,

Manuel²,

Meganathan³

et al. 2022

Mathematical Problems in Engineering

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In this research work, the aim is to develop the fractional proportional delta operator and present the generalized discrete Laplace transform and its convolution with the newly introduced fractional proportional delta operator. Moreover, this transform is a connection between Sumudu and Laplace transforms, which yields several applications in pure and applied science. The research work also investigates the fractional proportional differences and its sum on Riemann–Liouville and Mittag–Leffler functions. As an application of this research is to find new results and properties of fractional Laplace transform, the comparison of the existing results with this research work is also done. Moreover, we used the two types of solutions, namely, closed and summation forms in Laplace transform and verified with numerical results.

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Section: Introductionmentioning

confidence: 99%