Archive:: Pure and Applied Mathematics Journal:: Science Publishing Group

Volume 10, Issue 2, April 2021

Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative

Jagdish Ashruba Nanware

Issue: Volume 10, Issue 2, April 2021

Pages: 38-48

Received: 26 January 2021

Accepted: 14 February 2021

Published: 26 March 2021

DOI: 10.11648/j.pamj.20211002.11

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Abstract: In this paper, qualitative properties such as existence-uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative with initial conditions have been studied. Lower and upper solutions are defined for the problem under investigation. Comparison results are used to develop monotone technique for ... Show More

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Unstructured and Semi-structured Complex Numbers: A Solution to Division by Zero

Peter Jean-Paul, Shanaz Wahid

Issue: Volume 10, Issue 2, April 2021

Pages: 49-61

Received: 16 April 2021

Accepted: 30 April 2021

Published: 8 May 2021

DOI: 10.11648/j.pamj.20211002.12

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Abstract: Most mathematician, have accepted that a constant divided by zero is undefined. However, accepting this situation is an unsatisfactory solution to the problem as division by zero has arisen frequently enough in mathematics and science to warrant some serious consideration. The aim of this paper was to propose and prove the existence of a new number... Show More

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A Speedy New Proof of the Riemann's Hypothesis

Jean-Max Coranson-Beaudu

Issue: Volume 10, Issue 2, April 2021

Pages: 62-67

Received: 20 March 2021

Accepted: 24 April 2021

Published: 14 May 2021

DOI: 10.11648/j.pamj.20211002.13

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Abstract: In this paper we show that Riemann's function (xi), involving the Riemann’s (zeta) function, is holomorphic and is expressed as a convergent infinite polynomial product in relation to their zeros and their conjugates. Our work will be done on the critical band in which non-trivial zeros exist. Our approach is to use the properties of power series a... Show More

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