This article explores the Hilfer fractional derivative within the context of fractional differential equations and investigates a mathematical model formulated as a three-point boundary value problem ...(BVP). The primary focus is on the application of these models to analyze the jet flow of the Antarctic Circumpolar Current. The study establishes the existence of stream functions using Schaefer’s fixed point theorem under the assumption of the continuity of the vorticity function
Φ
. Furthermore, the article delves into the existence and uniqueness results of the stream functions by employing the Banach fixed point theorem. This analysis is conducted under the condition that the vorticity function
Φ
is Lipschitz continuous with respect to the stream function. Additionally, the stability of the stream functions of the BVP is explored through Ulam–Hyers and generalized Ulam–Hyers stability analyses. In contrast to the foundational results presented for the three-point BVP, the article includes illustrative examples aimed at validating the findings.
This manuscript is concerned about the study of the existence of solutions for the class of nonlinear neutral Caputo-Hadamard fractional differential equations including integral terms. In order to ...establish the necessary conditions of solvability for the proposed problem, we apply the semi-group property of Hadamard fractional integral operator. Also, under the appropriate conditions, we demonstrate that the solution set for the proposed problem is non-empty by using Arzelá-Ascoli theorem and the method of upper and lower solutions. In contrast to the fundamental results graphical example is also presented in order to validate the findings.
This article primarily focuses on the single-valued and multi-valued cases of the class of nonlinear Caputo two-term fractional differential equation with three-point integral boundary conditions. In ...the single-valued case, we employ Schaefer’s fixed point theorem and the Banach fixed point theorem to establish results regarding the existence and uniqueness of solutions, using linear growth and Lipschitz conditions. Furthermore, we delve into the stability analysis of the single-valued problem using Ulam–Hyers and Ulam–Hyers–Rassias stabilities. In addition to the above, we address the multi-valued scenario and provide results on the existence of solutions. This is achieved by employing the Covitz–Nadler FPT and the nonlinear alternative for contractive maps. As an application of our fundamental findings, we present illustrative examples that validate our results. These examples have been implemented using MATLAB.
In this manuscript, we have studied the coupled system of Hilfer fractional differential equations with non-local conditions. We have used the Leray-alternative Schauder’s and the Contraction ...principle to obtain the results on the existence and uniqueness of the solution of the proposed problem in the weighted space of continuous functions. For the defined problem, sufficient conditions have also been developed to determine the Ulam stability of the solution. The key conclusions are well-illustrated with examples.
The mechanisms of endosomal fission are poorly understood. In this study, it was demonstrated that the ATPase EHD1 is linked to the actin cytoskeleton via an interaction with Coronin2A. Depletion of ...the latter impairs recycling of clathrin-independent cargo and delays internalization of clathrin-dependent cargo by impeding endosomal fission.
Fission of transport vesicles from endosomes is a crucial step in the recycling of lipids and receptors to the plasma membrane, but this process remains poorly understood. Although key components of the fission machinery, including the actin cytoskeleton and the ATPase Eps15 homology domain protein 1 (EHD1), have been implicated in endosomal fission, how this process is coordinately regulated is not known. We have identified the actin regulatory protein Coronin2A (CORO2A) as a novel EHD1 interaction partner. CORO2A localizes to stress fibers and actin microfilaments but also can be observed in partial overlap with EHD1 on endosomal structures. siRNA knockdown of CORO2A led to enlarged lamellae-like actin-rich protrusions, consistent with a role of other Coronin family proteins in attenuating actin-branching. Moreover, CORO2A depletion also caused a marked decrease in the internalization of clathrin-dependent cargo but had little impact on the uptake of clathrin-independent cargo, highlighting key differences in the role of branched actin for different modes of endocytosis. However, CORO2A was required for recycling of clathrin-independent cargo, and its depletion led to enlarged endosomes, supporting a role for CORO2A in the fission of endosomal vesicles. Our data support a novel role for CORO2A in coordinating endosomal fission and recycling with EHD1.
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Following endocytosis, receptors that are internalized to sorting endosomes are sorted to different pathways, in part by sorting nexin (SNX) proteins. Notably, SNX17 interacts with a multitude of ...receptors in a sequence-specific manner to regulate their recycling. However, the mechanisms by which SNX17-labeled vesicles that contain sorted receptors bud and undergo vesicular fission from the sorting endosomes remain elusive. Recent studies suggest that a dynamin-homolog, Eps15 homology domain protein 1, catalyzes fission and releases endosome-derived vesicles for recycling to the plasma membrane. However, the mechanism by which EHD1 is coupled to various receptors and regulates their recycling remains unknown. Here we sought to characterize the mechanism by which EHD1 couples with SNX17 to regulate recycling of SNX17-interacting receptors. We hypothesized that SNX17 couples receptors to the EHD1 fission machinery in mammalian cells. Coimmunoprecipitation experiments and in vitro assays provided evidence that EHD1 and SNX17 directly interact. We also found that inducing internalization of a SNX17 cargo receptor, low-density lipoprotein receptor–related protein 1 (LRP1), led to recruitment of cytoplasmic EHD1 to endosomal membranes. Moreover, surface rendering and quantification of overlap volumes indicated that SNX17 and EHD1 partially colocalize on endosomes and that this overlap further increases upon LRP1 internalization. Additionally, SNX17-containing endosomes were larger in EHD1-depleted cells than in WT cells, suggesting that EHD1 depletion impairs SNX17-mediated endosomal fission. Our findings help clarify our current understanding of endocytic trafficking, providing significant additional insight into the process of endosomal fission and connecting the sorting and fission machineries.
In this paper, the authors have proposed the qualitative properties for the solution of the Hilfer implicit fractional differential equations (HIFDE) of order 1<ϱ≤2 involving nonlocal boundary ...conditions using fixed point theory. By imposing the growth conditions on a non-linear function the sufficient condition existence of a solution for the assumed problem is given by using Schaefer's fixed point theorem. The result for the existence and uniqueness of the solution has been established utilizing the Banach contraction principle using the Lipschitz property and following the existence and uniqueness result, a priori bound of the solution is also given. In addition to existence and uniqueness results, the Ulam-Hyers and Generalized Ulam-Hyers stability analysis for the solutions of HIFDE is also provided. Some examples are presented in order to demonstrate the applications of our findings.
In this article, we consider the second‐order nonautonomous integro‐differential system with finite delay and noninstantaneous impulse. The aim of this paper is to establish the approximate ...controllability result for the proposed control problem. We use the evolution operator and Schauder's fixed‐point approach for proving our main result. Also, we provide an example to illustrate our main result.
Background: Status dystonicus is a life-threatening, underrecognized movement disorder emergency. We aimed to ascertain the etiology, clinical presentation, complications, and outcomes of status ...dystonicus in children and reviewed the literature for similar studies. Methods: Records of all children aged <14 years admitted to a single center with status dystonicus between 2014 and 2018 were reviewed. Results: Twenty-four children (75% male) were identified with status dystonicus. The annual incidence rate was 0.05 per 1000 new admissions <12 years of age. The mean age at presentation was 6.3 ± 3.6 years. Median duration of hospital stay was 10.5 days (interquartile range 5-21.7). The severity of dystonia at presentation was grade 3 (n = 9; 37.5%) and 4 (n = 9; 37.5%). The most common triggering factor was intercurrent illness/infection (n = 18; 75%). The most common underlying etiologies were cerebral palsy (n = 8; 33.3%), complicated tubercular meningitis (n = 3; 12.5%), and mitochondrial disorders (n = 3; 12.5%). Basal ganglia involvement was seen in 15 cases (62.5%). Respiratory and/or bulbar compromise (n = 20; 83.3%) and rhabdomyolysis (n = 15; 62.5%) were most commonly seen. Oral trihexyphenidyl (96%) followed by oral or intravenous diazepam (71%), oral baclofen (67%), and midazolam infusion (54%) were the most common drugs used. Clonidine was used in 33% cases, without any significant side effects. Three children died owing to refractory status dystonicus and its complications; the mortality rate was 12.5%. Conclusion Status dystonicus is a neurologic emergency in children with severe dystonia, with significant complications and a high mortality rate. Static and acquired disorders are more common than heredo-familial causes. Identification and treatment of infection in children is important as the majority of cases are triggered by an intercurrent infection.
The sphenoid sinus (SS) is one of the four paired paranasal sinuses (PNSs) within the sphenoid bone body. Isolated pathologies of sphenoid sinus are uncommon. The patient may have various ...presentations like headache, nasal discharge, post nasal drip, or non-specific symptoms. Although rare, potential complications of sphenoidal sinusitis can range from mucocele to skull base or cavernous sinus involvement, or cranial neuropathy. Primary tumors are rare and adjoining tumors secondarily invading the sphenoid sinus is seen. Multidetector computed tomography (CT) scan and magnetic resonance imaging (MRI) are the primary imaging modalities used to diagnose various forms of sphenoid sinus lesions and complications. We have compiled anatomic variants and various pathologies affecting sphenoid sinus lesions in this article.
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