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We use the modification of Krasnoselskii's fixed point theorem due to T. A. Burton ( [1] Theorem 3) to show that the totally nonlinear difference equation with functional delay Δx (t) = -a (t) x3 (t + 1) + G (t, x3 (t), x3 (t - g (t))), ∀t ϵ ℤ, has periodic solutions. We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying Krasnoselskii-Burton theorem. Finally, an example is given to illustrate our result. [ABSTRACT FROM AUTHOR]

In this work, the hybrid fixed point theorem of Krasnoselskii is used to prove the existence of periodic solutions of the second-order nonlinear neutral differential equation d¹÷ dt² x(t) + p(t) d÷dt x(t) + q(t)x(t) = d÷dt g(t, x(t - Τ(t))) + f(t, x(t), x(t - Τ (t))). We transform the problem into an integral equation and uniqueness of the periodic solution, by means of the contraction mapping principle. [ABSTRACT FROM AUTHOR]

In this present manuscript, by applying fractional quantum calculus, we study a nonlinear fractional pantograph q-difference equation with nonlocal boundary conditions. We prove the existence and uniqueness results by using the well-known fixed-point theorems of Schaefer and Banach. We also discuss the Ulam–Hyers stability of the mentioned pantograph q-difference problem. Lastly, the paper includes pertinent examples to support our theoretical analysis and justify the validity of the results. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for a generalized sequential Caputo-type fractional neutral differential inclusion with generalized integral conditions. The used fractional operator has the generalized kernel in the format of (ϑ (t) − ϑ (s)) along with differential operator 1 ϑ ′ (t) d d t . We obtain existence results for two cases of convex-valued and nonconvex-valued multifunctions in two separated sections. We derive our findings by means of the fixed point principles in the context of the set-valued analysis. We give two suitable examples to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we debate the existence of solutions for a nonlinear Hilfer fractional differential inclusion with nonlocal Erdélyi–Kober fractional integral boundary conditions (FIBC). Both cases of convex- and nonconvex-valued right-hand side are considered. Our obtained results are new in the framework of Hilfer fractional derivative and Erdélyi–Kober fractional integral with FIBC via the fixed point theorems (FPTs) for a set-valued analysis. Some pertinent examples demonstrating the effectiveness of the theoretical results are presented. [ABSTRACT FROM AUTHOR]

In this paper we study the existence and uniqueness of positive solutions for a class of nonlinear Caputo-Hadamard fractional differential equations by using the method of upper and lower solutions and Schauder and Banach fixed point theorems. [ABSTRACT FROM AUTHOR]