Leibniz's Influence on the Evolution of Fractional Calculus: Bridging Classical and Modern Perspectives.

The development of calculus marks one of the most pivotal milestones in the history of mathematics, with Gottfried Wilhelm Leibniz (1646–1716) being a key figure in its early advancement. This paper examines Leibniz's role in the development of fractional calculus, a field of mathematical analysis that extends the traditional concepts of differentiation and integration to non-integer orders. Although Leibniz did not fully develop fractional calculus, his ideas and notations laid an essential foundation for its future growth. This study delves into Leibniz's impact on fractional calculus, connecting classical insights with modern developments, and underscores how his vision continues to influence contemporary research in this field.