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All Journal Journal of International Islamic Law, Human Right and Public Policy
Muneer Ahmad Sofi
Unknown Affiliation
Religion Law, Crime, Criminology & Criminal Justice

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THE HISTORY AND DEVELOPMENT OF PRIME NUMBERS Muneer Ahmad Sofi; Sobiya Jan
Journal of International Islamic Law, Human Right and Public Policy Vol. 3 No. 1 (2025): March
Publisher : PT. Radja Intercontinental Publishing

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59733/jishup.v3i1.119

Abstract

Prime numbers have captivated mathematicians for centuries due to their foundational role in number theory and their extensive applications in fields such as cryptography, computer science, and pure mathematics. This paper traces the historical development of prime numbers, beginning with early explorations in ancient Greece and continuing through significant advancements in modern mathematics. Key contributions from renowned mathematicians such as Euclid, Euler, Gauss, and Riemann are discussed, as well as the impact of prime numbers on contemporary technologies, particularly in encryption and computational research. The evolution of prime number theory, including ongoing research on the Riemann Hypothesis, is explored to emphasize the ongoing relevance and mystery of primes in both mathematics and technology.
Laplace transform and its applications to Fractional differential equations Muneer Ahmad Sofi; Sobiya Jan
Journal of International Islamic Law, Human Right and Public Policy Vol. 3 No. 2 (2025): June
Publisher : PT. Radja Intercontinental Publishing

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59733/jishup.v3i2.138

Abstract

This paper investigates the application of the Laplace transform method in solving fractional differential equations. It establishes sufficient conditions under which the Laplace transform provides a rational approach to these problems. Key definitions and properties of fractional calculus, including the Riemann-Liouville and Caputo fractional derivatives, are discussed. Several lemmas are proved to facilitate the computation of inverse Laplace transforms involving fractional operators. The effectiveness of the method is demonstrated through examples of solving linear fractional differential equations with exact solutions. The study concludes that while the Laplace transform is well-suited for fractional differential equations with constant coefficients, its applicability is limited by the nature of the forcing terms.
Co-Authors Sobiya Jan