‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎By applying Kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function‎. ‎Then the Arzela--Ascoli theorem is used to take $C^1$ ...

This article studies the existence of nonnegative solutions for a boundary value problem (BVP) of nonlinear fractional differential equations. Some new existence results are obtained by applying Kranoselskii‘s fixed–point theorem in a cone. First we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function. Then the Arzela–Ascoli theorem is used to take...

In this work, an initial value problem is discussed for a fractional differential equation of variable-order. By means of some analysis techniques and Arzela-Ascoli theorem, existence result of solution is obtained; Using the upper solutions and lower solutions and monotone iterative method, uniqueness existence results of solutions are obtained.

‎in this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎by applying kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary bvp formulated by truncating the response function‎. ‎then the arzela--ascoli theorem is used to take $c^1$ ...

This paper deals with the dynamics of stochastic delay lattice systems fractional discrete Laplacian driven by nonlinear noise. The existence a invariant measure for nonlocal is established under certain conditions. idea uniform estimates on tails solutions, technique diadic division and Arzela-Ascoli theorem are employed to show tightness family probability distributions solutions.

In this paper, we study the existence and multiplicity of positive solutions for semi-linear elliptic equations with a sign-changing weight function in weighted Sobolev spaces. By investigating the compact embedding theorem and based on the extraction of the Palais-Smale sequence in the Nehari manifold which is a subset of the weighted Sobolev spaces, we derive the existence of the multiple pos...

In this paper, using Caputo-Fabrizio fractional derivative, we obtain some new results for the existence and uniqueness of solutions differential equation with nonlocal initial value about order 0 < ? 1 . These are applied help Arzela-Ascoli theorem Schauder fixed point. Also based on ?-contractive maps such problems, unique has been introduced proved. Finally, illustrative example is consid...