AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.
AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.
In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the relevant literature. Example illustrating the results is included.
In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in
the state variable. We deal with the case of a fixed terminal time, as well
as the case of random terminal time. The need for this type of extension
of the classical existence and uniqueness results comes from the desire to
provide a probabilistic representation of the solutions of semilinear partial
differential equations in the spirit of a nonlinear Feynman-Kac formula.
Indeed, in many applications of interest, the nonlinearity is polynomial,
e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.
AbstractWe study a nonlocal problem for ordinary differential equations of {2n}-order with involution. Spectral properties of the operator of this problem are analyzed and conditions for the existence and uniqueness of its solution are established. It is also proved that the system of eigenfunctions of the analyzed problem forms a Riesz basis.
Existence and uniqueness of fractional mixed type integro-differential equations with non-instantaneous impulses through sectorial operator