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

J. Leo Amalraj, M. Maria Susai Manuel, M. Meganathan, M. Syed Ali and Thanin Sitthiwirattham

Mathematical Problems in Engineering, 2022, vol. 2022, 1-10

Abstract: 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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:4849312

DOI: 10.1155/2022/4849312

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