On fractional Langevin equation involving two fractional orders in different intervals

In this paper, we study a nonlinear Langevin equation involving two fractional orders  α ∈ (0; 1] and β ∈ (1; 2] with initial conditions. By means of an interesting fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. Some illustrative numerical examples are also discussed.&nbsp

Existence of solutions of infinite system of nonlinear sequential fractional differential equations

Abstract In a recent paper (Filomat 32:4577–4586, 2018) the authors have investigated the existence and uniqueness of a solution for a nonlinear sequential fractional differential equation. To present an analytical improvement for Fazli–Nieto's results with some conditions removed based on a new technique is the main objective of this paper. In addition, we introduce an infinite system of nonlinear sequential fractional differential equations and discuss the existence of a solution for them in the classical Banach sequence spaces c 0 $c_{0}$ and ℓ p $\ell_{p}$ by applying the Darbo fixed point theorem. Moreover, the proposed method is applied to several examples to show the clarity and effectiveness

Comparison of MCNPX and EGSnrc Monte Carlo Codes in the Calculation of Nano-Scaled Absorbed Doses and Secondary Electron Spectra around Clinically Relevant Nanoparticles

Purpose: Absorbed dose enhancement due to the presence of high atomic number nanoparticles (NP)s has been estimated and modeled by Monte Carlo (MC) simulation methods. In the current study, two MC codes of MCNPX and EGSnrc codes were compared by calculation of secondary electron energy spectra and nano-scaled dose values around four types of spherical NPs. Materials and Methods: The MC model was composed of a spherical nanoparticle with a diameter of 50 nm and mono-energetic sources of photons with energies of 30,60, and 100 keV. The secondary electrons emitted from the nanoparticle were scored on the nanoparticle surface and the delivered dose to water around the nanoparticle was tallied using concentric shells with a thickness of 25 nm. Four different elements were used as materials of NPs, including Gold, Bismuth, Gadolinium, and Hafnium. Results: Our results showed a considerable difference in the number of emitted electrons per incident photon between the two codes. There were also discrepancies between the two codes in the energy spectra of secondary electrons. Calculated radial dose values around NPs in nano-scale had a similar pattern for both codes. However, significant differences existed for some elements. Conclusion: It can be concluded that the results of nano-scaled MC modeling for nanoparticle-based radiation therapy are dependent on the code type and its algorithm for electron transport as well as exploited cross-section libraries

Cancer Risk Assessment due to Accidental Exposure inside Neutron Laboratories using BEIR VII Model

Introduction: Environmental and occupational human exposure from neutron source can lead to the serious biologic effects. The aim of this study is to evaluate the cancer incidence risk for various human organs at different neutron dose levels due to exposure from an Americium-241/Beryllium (Am-241/Be), a standard neutron source for calibration purposes. Material and Methods: We measured ambient dose equivalent H*(10) at different distances from Am-241/Be mixed neutron source by Berthold LB 6411 detector and determined cancer incidence risk for different organs of both male and female subjects at different neutron exposure levels by BEIR VII model. Results: Exposure age had a reverse impact on cancer incidence risk of different organs. We found that as H*(10) increases, cancer incidence risk increments as well. Colon (for men) and bladder (for women) had the highest sensitivity to neutron exposure, while prostate and uterus showed the lowest risk of cancer incidence among male and female subjects, respectively. Conclusion: Older exposed persons are at a lower risk of cancer incidence. The risk of cancer incidence for various organs is considerably associated with gender, such that radiation sensitivity of female organs was higher at all the measured neutron dose levels

On the new Hyers–Ulam–Rassias stability of the generalized cubic set-valued mapping in the incomplete normed spaces

We present a novel generalization of the Hyers–Ulam–Rassias stability definition to study a generalized cubic set-valued mapping in normed spaces. In order to achieve our goals, we have applied a brand new fixed point alternative. Meanwhile, we have obtained a practicable example demonstrating the stability of a cubic mapping that is not defined as stable according to the previously applied methods and procedures

Evaluation of dosimetric properties of shielding disk used in intraoperative electron radiotherapy: A Monte Carlo study

A shielding disk is used for IOERT procedures to absorb radiation behind the target and protect underlying healthy tissues. Setup variation of shielding disk can affect the corresponding in-vivo dose distribution. In this study, the changes of dosimetric parameters due to the disk setup variations is evaluated using EGSnrc Monte Carlo (MC) code. The results can help treatment team to decide about the level of accuracy in the setup procedure and delivered dose to the target volume during IOERT. © 2018 Elsevier Lt

A fixed point problem via simulation functions in incomplete metric spaces with its application

In this paper, firstly, we review the notion of the SO-complete metric spaces. This notion let us to consider some fixed point theorems for single-valued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of A.H. Ansari et al. [J. Fixed Point Theory Appl. (2017), 1145–1163], we obtain that an existence and uniqueness result for the following problem: finding x ∈ X such that x = T x, Ax R₁ Bx and Cx R₂ Dx, where (X, d) is an incomplete metric space equipped with the two binary relations R₁ and R₂, A, B, C, D : X → X are discontinuous mappings and T : X → X satisfies in a new contractive condition. This result is a real generalization of main theorem of A.H. Ansari’s. Finally, we provide some examples for our results and as an application, we find that the solutions of a differential equation.Publisher's Versio