Advanced Topics on Caputo Tempered Fractional Differential Equations with Applications

This book offers a unified and rigorous treatment of nonlinear differential equations involving the Caputo tempered fractional derivative and its generalizations.Spanning nine chapters, the authors systematically develop analytical methods for solving a wide variety of problems, including those with nonlocal, impulsive, periodic and delayed structures, within both deterministic and random settings.Each chapter is dedicated to a particular class of problems, beginning with global convergence and uniqueness analysis for the successive approximations method and extending to systems with neutral and infinite delays, boundary value problems with impulses, and coupled systems.The analytical approaches employed throughout the book include a rich array of mathematical tools: fixed point theory (Banach, Schauder, Darbo, Monch, Schaefer, Sadovskii, and Krasnoselskii); coincidence degree theory; the method of upper and lower solutions; diagonalization techniques; and the measure of noncompactness