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9 articles for “Riemann equation”
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On the Formula for Distribution of Prime Numbers
Abstract: The detailed derivation of the distribution of prime numbers, the research result originally presented in the 2013’ monograph Study of Analytic Number Theory: Riemann’s Hypothesis and Prime Number Theorem with Addendum on Integer Partitions published with Cam- bridge International Science Publishing, is once again presented in this paper with the purpose to give an insight to unfamiliar authors.
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 1, Issue 1, 2014 · pp. 16–19 Read article
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Modified Riemann−Liouville Fractional Derivative and Differential Equation for a Class of New Levy-type Probabilities
Abstract: The aim of the present paper to obtained the solution of differential equations involving Modified Riemann-Liouville fractional derivative in addition to it Levy-type one sided probability density function. Some scientist studied a small number of interesting problems regarding diffusing processes in media with fractal geometry, and formulated fractional diffusion.
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 1, Issue 3, 2014 · pp. 42–44 Read article
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Riemannian Metric based Smart Senor for Testing Corona Virus
Abstract: This paper proposes an electronic device based on Riemannian metric for testing corona virus. Hamilton’s evolution equation based sensor presents the nodes of corona virus through the Riemannian metric. The initial position and terminal position of corona virus based interval is defined with respect to the time. This is measured by Riemannian metric. There exists the functional F, which is the probable structure of corona virus and its variant over …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 10, Issue 3, 2023 · pp. 37–42 Read article
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An Application of Fractional Calculus in L-R and C-R Circuit
Abstract: In this paper, we proposed a Fractional differential equation for the electrical L-R and C-R Circuit and obtained the solution in the form of Mittag-Leffler function.Keywords: Circuit analysis, L-R and C-R circuit, Fractional differential equation, Riemann-Liouville Fractional derivative, Laplace transform, Inverse Laplace transform.Mathematical Subject Classification: -26A33, 33E12, 44A10Cite this Article: Laxmi Morya, Manoj Sharma, Rajshree Mishra. An Application of Fractional Calculus in L-R andC-R Circuit. Research & Reviews: Discrete Mathematical …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 7, Issue 2, 2020 · pp. 14–17 Read article
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Computable Extension of New Advanced Fractional Kinetic Equation
Abstract: AbstractFirst, we obtain computable extensions of advanced fractional kinetic equation. The aim of this survey is to explore the behavior of physical and biological systems from the point of view of fractional calculus. Fractional calculus, integration and differentiation of an arbitrary or fractional order, provide new tools that expand the descriptive power of calculus beyond the familiar integer-order concepts of rates of change and area under a curve. Fractional calculus …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 2, 2017 · pp. 26–32 Read article
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Advanced Computable Extension of New Fractional Kinetic Equation
Abstract: AbstractThe aim of this work is to find advanced computable extension of kinetic equation with fractional calculus approach. Fractional calculus originated in 1695, shortly after the inversion of classical calculus. The pioneer researchers who studied it were Liouville, Riemann, Leibniz, etc. For a long time, fractional calculus has been regarded as a pure mathematical area without applications. But, in recent decades, such type of synergism has been changed. It has …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 3, 2017 · pp. 74–80 Read article
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Fractional Free Electron Laser Equation and K-Function
Abstract: AbstractIn this era, fractional free electron laser (FEL) equations are studied due to their utility and importance in mathematical physics and engineering. The aim of present paper is to find the solution of generalized fractional order free electron laser (FEL) equation, using K-function. The results obtained here are moderately universal in nature. Special cases, relating to the exponential function are also considered. The special functions were introduced in 18th century …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 2, 2017 · pp. 17–20 Read article
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Fractional Riemannian Fuzzy C-Means with Time-Series Regularization for Economic Manifold Forecasting
Abstract: A fractional Riemannian fuzzy c-means framework is proposed for uncertain economic forecasting on non-Euclidean data domains. Observations are represented on a Riemannian manifold, cluster centres are intrinsic prototypes, and a latent fuzzy regime signal is regularised by both autoregressive and fractional-memory penalties. The resulting objective couples geometric clustering with time-series consistency, thereby discouraging partitions that are locally plausible but temporally incoherent. Closed-form membership updates, exponential-map centre updates, normal equations for …
Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 · pp. 49–55 Read article
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Galois Theory and Ricci Flow Curvature Applications for Generating the Mandelbrot Set
Abstract: In this paper, an application of Galois theory is presented through Ricci flow curvature in Mandelbrot set. The Mandelbrot set is analyzed over Ricci flow equation for generating the fractal set simply. Although, the fractal set is generated as the points in the complex plane connected to the Julia set and approaches to infinity. This paper proposes an efficient method of fractal set generation based on onto-one correspondence between Ricci …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 9, Issue 3, 2022 · pp. 24–29 Read article