Nonlinear Fractional Differential Equations of Variable Order

Mohamed Said Souid is a Professor Doctor of Mathematics at the University of Tiaret, Algeria. He earned a magister degree in 2010 and a doctorate in mathematics in 2015 from Sidi Bel Abbes University, Algeria. Since 2010, he has been teaching at Ibn Khaldoun University in Tiaret. He specializes in nonlinear differential equations and fractional calculus, fields in which he has made significant research contributions. Throughout his academic career, Souid has developed a deep expertise in fractional differential equations, particularly focusing on variable-order operators and boundary value problems. His research has resulted in numerous publications that have advanced the understanding and applications of fractional calculus in mathematical analysis and applied sciences. Known for his dedication to education and research, Souid has mentored many students and contributed extensively to curriculum development in advanced mathematics. His work combines theoretical insights with practical applications, making him a respected figure in both the academic and research communities.Mustafa Inc is a Professor of Applied Mathematics at Fırat University in Elazığ, Türkiye. He obtained a PhD in Applied Mathematics from Fırat University in 2002. Professor Inc has contributed extensively to the study of analytical and numerical methods for solving complex mathematical equations, optical soliton, Lie symmetry and conservation laws, including solitary wave solutions and generalized functions. He has published numerous scientific articles in international journals and is recognized for his expertise in applied numerical mathematics. His academic career involves teaching a variety of mathematics courses while actively engaging in research projects and supervising graduate students. Mustafa Inc is noted for his scholarly impact within the field of mathematical sciences, holding a notable position among top mathematicians in Turkey and globally. His continuous dedication to advancing applied mathematics has made significant contributions to both theoretical and practical aspects of the discipline.Amar Benkerrouche is an Associate Professor at Djelfa University, Algeria, specializing in the applications of fractional calculus within the physical sciences. He has a PhD in mathematics, his work centers on modeling complex systems using advanced mathematical tools. Amar’s research integrates fractional differential equations to better describe phenomena in diverse scientific fields, contributing valuable insights into the behavior of complex and nonlinear systems. His expertise extends beyond pure mathematics, encompassing interdisciplinary collaborations that connect mathematical theory with practical challenges in applied sciences. Throughout his career, he has participated in various projects that bridge the gap between abstract mathematical concepts and their real-world applications, demonstrating his commitment to advancing both theory and practice. Amar’s work is marked by a strong focus on innovative modeling techniques, enabling more accurate and efficient representations of dynamic processes in physics and related disciplines.

• Preface. 1. Introduction. 2. Preliminary. 3. Initial and Terminal Value Problems of R-Liouville Fractional Differential Equations of Variable Order. 4. Problems for Caputo’s Fractional Differential Equations with Variable Order. 5. Initial and Terminal Value Problems of Hadamard Fractional Differential Equations of Variable Order. 6. Problems for Caputo-Hadamard Fractional Differential Equations with Variable Order. 7. Conclusion. References. Index.