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Outline

Title
Abstract
FAQs
Introduction
Special Cases
Conclusion
References
All Topics
Mathematics

International Bulletin of Mathematical Research Vol 1 Issue 1

Profile image of S. PurohitS. PurohitProfile image of Allied JournalsAllied Journals

Abstract

A remarkably large number of operational techniques have drawn the attention of several researchers in the study of sequences of functions and polynomials. In this sequel, here, we aim to introduce a new sequence of functions involving a product of the generalized Mittag-Leffler function by using operational techniques. Some generating relations and finite summation formula of the sequence presented here are also considered.

FAQs

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What is the significance of operational techniques in mathematical analysis?add

The research highlights that operational techniques simplify solving differential equations by transforming them into algebraic polynomial problems. This approach has been significantly developed by various researchers over the last four decades.

How do the new sequences of functions derived affect existing mathematical frameworks?add

The study introduces a new sequence involving the product of generalized Mittag-Leffler functions, enhancing existing operational techniques. This may potentially unify various mathematical models and extend applications in applied sciences.

What role do special functions play in operational calculus applications?add

The paper indicates that numerous operational techniques leverage special functions, which have practical applications across fields like physics and engineering. This is exemplified by the essential properties of the Mittag-Leffler function in solving fractional differential equations.

How were generating relations derived in the context of operational techniques?add

Generating relations were established using the operational technique of applying certain defined operators, leading to specific sequence evaluations. These relations, outlined in the proofs, facilitate further mathematical exploration within operational calculus.

What historical context surrounds the development of the Mittag-Leffler function?add

The Mittag-Leffler function, introduced by Gosta Mittag-Leffler in 1903, generalizes the exponential function and emerged as essential in fractional calculus. Its significance has intensified in the last two decades due to its relevance in complex systems across various disciplines.

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References (31)

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