Existence and uniqueness of mild solution for fractional integrodifferential equations.
Existence and uniqueness of solution for a class of nonlinear sequential differential equations of fractional order
Two-term semi-linear and two-term nonlinear fractional differential equations (FDEs) with sequential Caputo derivatives are considered. A unique continuous solution is derived using the equivalent norms/metrics method and the Banach theorem on a fixed point. Both, the unique general solution connected to the stationary function of the highest order derivative and the unique particular solution generated by the initial value problem, are explicitly constructed and proven to exist in an arbitrary...
Existence and uniqueness of solutions for the fractional integro-differential equations in Banach spaces.
Existence and uniqueness of solutions to fractional semilinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions.
Existence of convex and non convex local solutions for fractional differential inclusions.
Existence of discontinuous absolute minima for certain multiple integrals without growth properties
In the present paper the author discusses certain multiple integrals of the calculus of variations satisfying convexity conditions, and no growth property, and the corresponding Serrin integrals , to which the existence theorems in [3,4,5] do not apply. However, in the present paper, the integrals and are reduced to simpler form and to which the existence theorems above apply. Thus, we derive that , , we obtain the existence of the absolute minimum for the Serrin forms and , and...
Existence of local and global solutions to some impulsive fractional differential equation.
Existence of positive solution of a singular partial differential equation
Motivated by Vityuk and Golushkov (2004), using the Schauder Fixed Point Theorem and the Contraction Principle, we consider existence and uniqueness of positive solution of a singular partial fractional differential equation in a Banach space concerning with fractional derivative.
Existence of positive solutions for fractional differential equations with Riemann-Liouville left-hand and right-hand fractional derivatives.
Existence of positive solutions for multiterm fractional differential equations of finite delay with polynomial coefficients.
Existence of positive solutions for multi-term non-autonomous fractional differential equations with polynomial coefficients.
Existence of positive solutions for singular fractional differential equations.
Existence of positive solutions to singular -Laplacian general Dirichlet boundary value problems with sign changing nonlinearity.
Existence of solutions for fractional differential inclusions with antiperiodic boundary conditions.
Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces
We study the existence of mild solutions for a class of impulsive fractional partial neutral integro-differential inclusions with state-dependent delay. We assume that the undelayed part generates an α-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by means of the fixed point theorem for discontinuous multi-valued operators due to Dhage and properties of the α-resolvent operator. An example is given to illustrate the...
Existence of solutions for integrodifferential equations of fractional order with antiperiodic boundary conditions.
Existence of solutions for nonlinear fractional integro-differential equations with three-point nonlocal fractional boundary conditions.
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 differential inclusions with fractional order and impulses.