Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 2025 12 24 A new study for various solutions of the extended Korteweg-de Vries equation with conformable derivative 10372 10.22075/ijnaa.2024.35417.5276 EN Ahmad Sharif Department of Mathematics, Faculty of Sciences, Gonbad Kavous University, Gonbad, Iran 0000-0002-6598-7139 Aynaz Ataie Department of Mathematics, Faculty of Sciences, Gonbad Kavous University, Gonbad, Iran Razeieh Farokhzad Rostami Department of Mathematics, Faculty of Sciences, Gonbad Kavous University, Gonbad, Iran Journal Article 2024 09 23 The extended fractional Korteweg–de Vries (K-dV) equation is examined in this paper through the Jacobi elliptic method. This approach is a powerful technique capable of generating multiple forms of solutions, making it highly useful for representing various types of wave behaviors. The graphical interpretations clearly illustrate the dynamics of the obtained solutions. To the best of our knowledge, this work is the first to provide exact analytical solutions for the fractional K-dV equation, and the findings hold significant theoretical and practical value in areas such as optical signal transmission, plasma wave dynamics, and ocean wave propagation. https://ijnaa.semnan.ac.ir/article_10372_f1ab58817d7385758d31890a4bca9968.pdf