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Abstract: In this paper, by using the Schauder fixed point theorem, we study the existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations and obtain some new results. [Copyright &y& Elsevier]

Abstract: In this paper, we first present a version of Filippov’s Theorem for fractional semilinear differential inclusions of the form, where is the Caputo fractional derivative and is a set-valued map. After several existence results, the compactness of solutions sets is also investigated. Some results from topological fixed point theory together with notions of measure of noncompactness are used. [Copyright &y& Elsevier]

Abstract: In this paper, by using the fixed point theory, we study the existence and uniqueness of initial value problems for nonlinear fractional differential equations and obtain a new result. [Copyright &y& Elsevier]

Abstract: In the light of the fixed point theorems, we analytically establish the conditions for the uniqueness of solutions as well as the existence of at least one solution in the nonlocal boundary value problem for a specific kind of nonlinear fractional differential equation. Furthermore, we provide a representative example to illustrate a possible application of the established analytical results. [Copyright &y& Elsevier]

Abstract: In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential equations with variable times involving the Caputo fractional derivative. [Copyright &y& Elsevier]

Abstract: In this paper, we first present an impulsive version of the Filippov–Ważewski theorem and a continuous version of the Filippov theorem for fractional differential inclusions of the form where denotes the Caputo fractional derivative, and is a set-valued map. The functions characterize the jump of the solutions at impulse points . Additional existence results are obtained under both convexity and nonconvexity conditions on the multivalued right-hand side. The proofs rely on the nonlinear alternative of Leray–Schauder type, a Bressan–Colombo selection theorem, and Covitz and Nadler’s fixed point theorem for multivalued contractions. The compactness of the solution set is also investigated. Finally, some geometric properties of solution sets, sets, acyclicity and contractibility, corresponding to Aronszajn–Browder–Gupta type results, are obtained. We also consider the impulsive fractional differential equations and where is a single map. Finally, we extend the existence result for impulsive fractional differential inclusions with periodic conditions, where is a multivalued map. The study of the above problems use an approach based on the topological degree combined with a Poincaré operator. [Copyright &y& Elsevier]

Abstract: In this paper, we establish sufficient conditions for existence and uniqueness of solutions for some nondensely defined semilinear functional differential equations involving the Riemann–Liouville derivative. Our approach is based on integrated semigroup theory, the Banach contraction principle, and the nonlinear alternative of Leray–Schauder type. [Copyright &y& Elsevier]