Nonlinear Fractional Differential Equations of Variable Order
暫譯: 變階非線性分數微分方程

本書探討變階分數微分方程的理論及應用。內容深入數學基礎，包括符號、定義及關鍵定理，同時也涉及各個領域的實際應用。本書將引導讀者從基本概念到進階主題，適合數學、工程及應用科學的研究人員和研究生。每一章節都包含示例和數值應用，以加強理論概念的理解。本書還強調穩定性分析及固定點定理在解決分數微分方程中的應用。

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.

**Mohamed Said Souid** 是阿爾及利亞提亞雷特大學的數學教授。他於2010年獲得碩士學位，並於2015年在阿爾及利亞西迪·貝爾·阿貝斯大學獲得數學博士學位。自2010年以來，他一直在提亞雷特的伊本·哈爾敦大學任教。他專注於非線性微分方程和分數微積分，這些領域中他做出了重要的研究貢獻。在他的學術生涯中，Souid在分數微分方程方面積累了深厚的專業知識，特別是專注於變階算子和邊值問題。他的研究產生了許多出版物，推進了分數微積分在數學分析和應用科學中的理解和應用。Souid以對教育和研究的奉獻而聞名，指導了許多學生，並在高等數學課程開發中做出了廣泛的貢獻。他的工作結合了理論見解和實際應用，使他在學術界和研究界都受到尊敬。

**Mustafa Inc** 是土耳其埃拉澤的菲拉特大學應用數學教授。他於2002年在菲拉特大學獲得應用數學博士學位。Inc教授在解決複雜數學方程的分析和數值方法、光學孤子、李對稱和守恆定律的研究中做出了廣泛的貢獻，包括孤立波解和廣義函數。他在國際期刊上發表了許多科學文章，並因其在應用數值數學方面的專業知識而受到認可。他的學術生涯涉及教授各種數學課程，同時積極參與研究項目並指導研究生。Mustafa Inc在數學科學領域的學術影響力顯著，在土耳其及全球的頂尖數學家中佔有重要地位。他對推進應用數學的持續奉獻對該學科的理論和實踐方面都做出了重要貢獻。

**Amar Benkerrouche** 是阿爾及利亞傑爾法大學的副教授，專注於分數微積分在物理科學中的應用。他擁有數學博士學位，工作重點是使用先進的數學工具對複雜系統進行建模。Amar的研究整合了分數微分方程，以更好地描述各種科學領域中的現象，為複雜和非線性系統的行為提供了有價值的見解。他的專業知識超越了純數學，涵蓋了將數學理論與應用科學中的實際挑戰相連接的跨學科合作。在他的職業生涯中，他參與了多個項目，彌合了抽象數學概念與其現實應用之間的鴻溝，展現了他對推進理論和實踐的承諾。Amar的工作以強調創新建模技術為特點，使得在物理及相關學科中對動態過程的表徵更加準確和高效。