Existence of solutions for a nonlinear fractional order differential equation.
Existence of solutions for fractional differential inclusions with boundary conditions.
Existence of solutions for fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions
In this paper, we discuss the existence of solutions for a boundary value problem of fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions. Our results include the cases when the multivalued map involved in the problem is (i) convex valued, (ii) lower semicontinuous with nonempty closed and decomposable values and (iii) nonconvex valued. In case (i) we apply a nonlinear alternative of Leray-Schauder type, in the second case we combine the nonlinear alternative...
Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations.
Existence of solutions of abstract fractional impulsive semilinear evolution equations.
Existence of solutions of generalized fractional differential equation with nonlocal initial condition
This paper is devoted to studying the existence of solutions of a nonlocal initial value problem involving generalized Katugampola fractional derivative. By using fixed point theorems, the results are obtained in weighted space of continuous functions. Illustrative examples are also given.
Existence of solutions of impulsive boundary value problems for singular fractional differential systems
A class of impulsive boundary value problems of fractional differential systems is studied. Banach spaces are constructed and nonlinear operators defined on these Banach spaces. Sufficient conditions are given for the existence of solutions of this class of impulsive boundary value problems for singular fractional differential systems in which odd homeomorphism operators (Definition 2.6) are involved. Main results are Theorem 4.1 and Corollary 4.2. The analysis relies on a well known fixed point...
Existence of solutions to anti-periodic boundary value problem for nonlinear fractional differential equations with impulses.
Existence of solutions to fractional mixed integrodifferential equations with nonlocal initial condition.
Existence of solutions to fractional order ordinary and delay differential equations and applications.
Existence of solutions to nonlinear Langevin equation involving two fractional orders with boundary value conditions.
Existence results for impulsive fractional differential equations with -Laplacian via variational methods
This paper presents several sufficient conditions for the existence of at least one classical solution to impulsive fractional differential equations with a -Laplacian and Dirichlet boundary conditions. Our technical approach is based on variational methods. Some recent results are extended and improved. Moreover, a concrete example of an application is presented.
Existence results for nonlocal boundary value problems for fractional differential equations and inclusions with fractional integral boundary conditions
This paper studies a new class of nonlocal boundary value problems of nonlinear differential equations and inclusions of fractional order with fractional integral boundary conditions. Some new existence results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also discussed.
Existence results for singular boundary value problem of nonlinear fractional differential equation.
Existence results for systems of conformable fractional differential equations
In this article, we study the existence of solutions to systems of conformable fractional differential equations with periodic boundary value or initial value conditions. where the right member of the system is -carathéodory function. We employ the method of solution-tube and Schauder’s fixed-point theorem.
Existence theory for sequential fractional differential equations with anti-periodic type boundary conditions
We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated) and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration...
Filippov's theorem for impulsive differential inclusions with fractional order.
Fractional BVPs with strong time singularities and the limit properties of their solutions
In the first part, we investigate the singular BVP , u(0) = A, u(1) = B, c D α u(t)|t=0 = 0, where is a continuous operator, α ∈ (0, 1) and a < 0. Here, c D denotes the Caputo fractional derivative. The existence result is proved by the Leray-Schauder nonlinear alternative. The second part establishes the relations between solutions of the sequence of problems , u(0) = A, u(1) = B, where a < 0, 0 < β n ≤ α n < 1, limn→∞ β n = 1, and solutions of u″+(a/t)u′ = f(t, u, u′) satisfying...
Fractional differential equation with the fuzzy initial condition.
Fractional differential equations in terms of comparison results and Lyapunov stability with initial time difference.