Search

In this paper, we study the existence and stability of solutions for impulsive pantograph fractional integro-differential equation via ψ-Hilfer fractional derivative in a appropriate Banach space. Our approach is based on fixed point theorems of Darbo’s and Mönch via Kuratowski measure of non-compactness. An example is given to illustrate our approach. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of nonlinear operators-the class of general historydependent operators. These are the operators defined on spaces of functions endowed with a structure of Banach space (the case of bounded interval of time) or Frechet space (the case of unbounded interval of time). We state and prove various properties of such operators, including fixed point properties. Moreover, we also study several classes of differential equations in Banach spaces, for which we our previous results can be applied. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the existence of positive solutions for the semipositone fractional boundary value problem with n point fractional integral boundary conditions. The existence of positive solutions is established using the five functionals fixed point theorem. An example is given to ratify that our main result is theoretically feasible. [ABSTRACT FROM AUTHOR]