*Correspondence: [email protected] School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, PR China Abstract In this paper, we study boundary-value problems for the following nonlinear fractional differential equations involving the Caputo fractional derivative: D0+x(t) = f (t, x(t), Dβ0+x(t)), t ∈ [0, 1], x(0) + x′(0) = y(x), ∫ 1 0 x(t)dt =m, x′′(0) = x′′′(0) = · · · = x(n–...

In this paper, we discuss the existence and uniqueness of solutions for boundary value problems Hilfer generalized proportional fractional differential equations with multi-point conditions. Firstly, consider scalar case which result is proved by using Banach’s fixed point theorem results are established via Krasnosel’skiĭ’s Leray–Schauder nonlinear alternative. We then establish an in Banach s...

In this paper we formulate and prove some xed and common xed pointTheorems for self-mappings dened on complete lower Transversal functionalprobabilistic spaces.

First of all, in this paper we obtain a perturbed version the geometric series theorem, which allows us to present an iterative numerical method approximate fixed point contractive affine operator. This result requires some approximations that using projections associated with certain Schauder bases. Next, algorithm is designed solution Fredholm’s linear integral equation, and illustrate behavi...

The purpose of this article is to discuss the existence, uniqueness, and Ulam–Hyers stability solutions a coupled system fractional differential equations with Erdélyi–Kober Riemann–Liouville integral boundary conditions. Banach fixed point theorem used prove uniqueness solutions, while Leray–Schauder alternative existence solutions. Furthermore, we conclude that solution discussed problem Hyer...

In this paper, we establish sufficient conditions for the existence of bounded solution a class boundary value problem nonlinear fractional differential equations involving Erdélyi-Kober operator on unbounded domain. Our results are based fixed point theorem Schauder combined with diagonalization argument method in special Banach space. To that end, an example is presented to illustrate usefuln...

In this paper, we establish existence and uniqueness results for single-valued as well multi-valued (k,ψ)-Hilfer boundary value problems of order in (1,2], subject to nonlocal integro-multi-point conditions. the case, use Banach Krasnosel’skiĭ fixed point theorems a Leray–Schauder nonlinear alternative derive results. For problem, prove two convex non-convex nature map involved problem by apply...

The existence of bounded nonoscillatory solutions of a higher-order nonlinear neutral delay difference equationΔ akn · · ·Δ a2nΔ a1nΔ xn bnxn−d f n, xn−r1n , xn−r2n , . . . , xn−rsn 0, n ≥ n0, where n0 ≥ 0, d > 0, k > 0, and s > 0 are integers, {ain}n≥n0 i 1, 2, . . . , k and {bn}n≥n0 are real sequences, ⋃s j 1{rjn}n≥n0 ⊆ Z, and f : {n : n ≥ n0} × R → R is a mapping, is studied. Some sufficient...

this paper studies a fractional boundary value problem of nonlineardifferential equations of arbitrary orders. new existence and uniquenessresults are established using banach contraction principle. other existenceresults are obtained using schaefer and krasnoselskii fixed point theorems.in order to clarify our results, some illustrative examples are alsopresented.

We investigate a class of singular m-point p-Laplacian boundary value problem on time scales with the sign changing nonlinearity. By using the well-known Schauder fixed point theorem and upper and lower solutions method, some new existence criteria for positive solutions of the boundary value problem are presented. These results are new even for the corresponding differential (T = R) and differ...