A hybrid method and applications for solving fractional order partial differential equations

This thesis develops hybrid and advanced methods for solving fractional differential equations using Caputo-Fabrizio derivatives and transforms. The study is organized into four main sections. The first section introduces fundamental concepts and practical applications to enhance understanding. The second section examines the definitions and properties of fractional derivatives, including Riemann-Liouville, Caputo, and Caputo-Fabrizio. In the third section, the proposed method is introduced and applied to key equations such as the Newell-Whitehead-Segel equation and the Geophysical Korteweg-de Vries (gKdV) equation. In the fourth section, the proposed methods offer accurate and efficient solutions, validated through comparisons with existing solutions and exact results in the literature. This research significantly contributes to fractional calculus by providing reliable tools for addressing complex systems in engineering, physics, and applied sciences.