Search Results (15)

This research introduces an innovative fractal–fractional synergy framework for multiscale analysis of stress field dynamics in geo-energy systems. By integrating fractional calculus with multiscale fractal dimension analysis, we develop a coupled approach examining stress redistribution patterns across different geological scales. The methodology combines fractal characterization of rock mechanical parameters with fractional-order stress gradient modeling, validated through integrated analysis of core testing, well logging, and seismic inversion data. Our fractal–fractional operators enable simultaneous characterization of stress memory effects and scale-invariant fracture propagation patterns. Key insights reveal the following: (1) Non-monotonic variations in rock mechanical properties (fractal dimension D = 2.31–2.67) correlate with oil–water ratio changes, exhibiting fractional-order transitional behavior. (2) Critical stress thresholds (12.19–25 MPa) for fracture activation follow fractional power-law relationships with fracture orientation deviations. (3) Fracture network evolution demonstrates dual-scale dynamics—microscale tip propagation governed by fractional stress singularities (order α = 0.63–0.78) and macroscale expansion obeying fractal growth patterns (Hurst exponent H = 0.71 ± 0.05). (4) Multiscale modeling reveals anisotropic development with fractal dimension increasing by 18–22% during multi-well fracturing operations. The fractal–fractional formalism successfully resolves the stress-shadow paradox while quantifying water channeling risks through fractional connectivity metrics. This work establishes a novel paradigm for coupled geomechanical–fluid dynamics analysis in complex reservoir systems. Full article

This paper is devoted to the analysis of a system of generalized variational inclusion problems involving $\alpha$-averaged and Cayley operators within the framework of a q-uniformly smooth Banach space. We demonstrate that the problem can be reformulated as an equivalent fixed-point equation and propose an iterative method based on the fixed-point approach to obtain the solution. Furthermore, we establish the existence of solutions and analyze the convergence properties of the proposed algorithm under suitable conditions. To validate the effectiveness of the proposed iterative method, we provide a numerical result supported by a computational graph and a convergence plot, illustrating its performance and efficiency. Full article

This paper explores the mild solutions of partial impulsive fractional integro-differential systems of order $1<\alpha <2$ in a Banach space. We derive the solution of the system under the assumption that the homogeneous part of the system admits an $\alpha$-resolvent operator. Krasnoselskii’s fixed point theorem is used for the existence of solution, while uniqueness is ensured using Banach’s fixed point theorem. The stability of the system is analyzed through the framework of Hyers–Ulam stability using Lipschitz conditions. Finally, examples are presented to illustrate the applicability of the theoretical results. Full article

The goal of this work is to introduce the notion of topological degree via the principle of the degree of nondensifiability (DND for short). We establish some new fixed point theorems, concerning, Schaefer’s fixed point theorem and the nonlinear alternative of Leray–Schauder type. As applications, we study the existence of mild solution of functional semilinear integro-differential equations. Full article

In this research paper, we investigate the controllability in the $\alpha$-norm of a coupled system of integrodifferential equations with state-dependent nonlocal conditions in generalized Banach spaces. We establish sufficient conditions for the system’s controllability using resolvent operator theory introduced by Grimmer, fractional power operators, and fixed-point theorems associated with generalized measures of noncompactness for condensing operators in vector Banach spaces. Finally, we present an application example to validate the proposed methodology in this research. Full article

The action of a noise operator on a code transforms it into a distribution on the respective space. Some common examples from information theory include Bernoulli noise acting on a code in the Hamming space and Gaussian noise acting on a lattice in the Euclidean space. We aim to characterize the cases when the output distribution is close to the uniform distribution on the space, as measured by the Rényi divergence of order $\alpha \in (1,\infty ]$. A version of this question is known as the channel resolvability problem in information theory, and it has implications for security guarantees in wiretap channels, error correction, discrepancy, worst-to-average case complexity reductions, and many other problems. Our work quantifies the requirements for asymptotic uniformity (perfect smoothing) and identifies explicit code families that achieve it under the action of the Bernoulli and ball noise operators on the code. We derive expressions for the minimum rate of codes required to attain asymptotically perfect smoothing. In proving our results, we leverage recent results from harmonic analysis of functions on the Hamming space. Another result pertains to the use of code families in Wyner’s transmission scheme on the binary wiretap channel. We identify explicit families that guarantee strong secrecy when applied in this scheme, showing that nested Reed–Muller codes can transmit messages reliably and securely over a binary symmetric wiretap channel with a positive rate. Finally, we establish a connection between smoothing and error correction in the binary symmetric channel. Full article

In this article, a nonlinear system of generalized ordered XOR-inclusion problems in Hilbert space is introduced and studied. Initially, we define the resolvent operator related to the $(\alpha ,\lambda )$-XOR-weak-ANODD multivalued mapping. Using the fixed point technique, we demonstrate the results of existence. In order to make the suggested system more realistic, we create the S-iterative algorithm and demonstrate that the sequence generated through this technique strongly converges with the proposed system’s solution. One example is provided in support of the existence result as well. Full article

A derivation of the dynamic model of a medium voltage vacuum circuit breaker and induction motor in space vectors in coordinates $\alpha \beta 0$ allow us to model switching transients in various dynamic states of the motor. In the case of the Clark transformation, the corresponding numerical integration technique can be selected including variable time-step integration techniques to avoid numerical instabilities due to the stiffness of the system. Assymetrical operations such as switching cause the power system to become unbalanced and the transformed equations $\alpha$, $\beta ,$ and $0$ are not uncoupled. Therefore, it is necessary to derive a coupling matrix between circuit breaker voltages and currents in the coordinate system $\alpha \beta 0$. The subject of our interest is switching overvoltages that arise when turning off small inductive currents by a vacuum circuit breaker. When deriving the model of a vacuum circuit breaker, all its properties encountered during this action are taken into account, i.e., current chop, virtual current chop, dielectric barrier in the circuit breaker and its recovery rate, and the ability of the vacuum circuit breaker to extinguish high frequency currents. Simulation results are compared with the measured results on a medium voltage motor as well as with the simulation results of the mathematical model of the test circuit according to IEC 62271-110 resolved using the nodal method (EMTP algorithm). Models are implemented in the MATLAB/Simulink programming environment. Full article

The management of post-operative (PO) pain has generally been shown to be inadequate; therefore, acquiring a novel understanding of PO pain mechanisms would increase the therapeutic options available. There is accumulating evidence to implicate N-methyl-d-aspartate (NMDA) receptors in the induction and maintenance of central sensitization during pain states by reinforcing glutamate sensory transmission. It is known that DMF protects from oxidative glutamate toxicity. Therefore, NMDA receptor antagonists have been implicated in peri-operative pain management. Recent advances demonstrated that dimethyl fumarate (DMF), a non-opioid and orally bioavailable drug, is able to resolve neuroinflammation through mechanisms that drive nociceptive hypersensitivity. Therefore, in this study, we evaluated the role of DMF on pain and neuroinflammation in a mouse model of PO pain. An incision of the hind paw was performed, and DMF at two different doses (30 and 100 mg/kg) was administered by oral gavage for five consecutive days. Mechanical allodynia, thermal hyperalgesia and locomotor dysfunction were evaluated daily for five days after surgery. Mice were sacrificed at day 7 following PO pain induction, and hind paw and lumbar spinal cord samples were collected for histological and molecular studies. DMF administration significantly reduced hyperalgesia and allodynia, alleviating motor disfunction. Treatment with DMF significantly reduced histological damage, counteracted mast cell activation and reduced the nuclear factor kappa-light-chain-enhancer of the activated B cell (NF-κB) inflammatory pathway, in addition to downregulating tumor necrosis factor-α (TNF-α), Interleukin-1β (Il-1β) and Il-4 expression. Interestingly, DMF treatment lowered the activation of NMDA receptor subtypes (NR2B and NR1) and the NMDA-receptor-interacting PDZ proteins, including PSD93 and PSD95. Furthermore, DMF interfered with calcium ion release, modulating nociception. Thus, DMF administration modulated PO pain, managing NMDA signaling pathways. The results suggest that DMF positively modulated persistent nociception related to PO pain, through predominantly NMDA-receptor-operated calcium channels. Full article

An exponential-type function was discovered to transform known difference formulas by involving a shifted parameter $\theta$ to approximate fractional calculus operators. In contrast to the known $\theta$ methods obtained by polynomial-type transformations, our exponential-type $\theta$ methods take the advantage of the fact that they have no restrictions in theory on the range of $\theta$ such that the resultant scheme is asymptotically stable. As an application to investigate the subdiffusion problem, the second-order fractional backward difference formula is transformed, and correction terms are designed to maintain the optimal second-order accuracy in time. The obtained exponential-type scheme is robust in that it is accurate even for very small $\alpha$ and can naturally resolve the initial singularity provided $\theta =-\frac{1}{2}$, both of which are demonstrated rigorously. All theoretical results are confirmed by extensive numerical tests. Full article

Economic dispatch optimization and power management are the main concerns for a microgrid (MG). They are always studied and are considered to achieve an efficient operation of the MG by simplifying the control process and decreasing losses. The integration of a small-scale wind turbine (SSWD) into a direct current (DC) MG has an impact on its power and energy management. Excess power produced by renewable energy sources (RESs) is one of the problems that face the reliability of the MG and should be resolved. For this reason, a supervisory system is suggested to manage the excess of power. During the supervision process, some criteria, such as the physical limits and tariffs of the components are taken into account. Then, the suggested power management strategy aims to achieve an instantaneous power balance considering a rule-based power and depends on the above-mentioned criteria. To better meet the power balance, it is necessary to explore the constraints related to the control and supervision of the studied DC MG. Performance measures include the overall system energy cost and renewable curtailment (renewable energy that cannot be utilized and should be limited). Thus, the power limitation strategy consists of using two types of “shedding coefficients”, $\alpha$ and $\gamma$, to calculate the power that should be limited from each RES in the case of energy surplus. Simulation tests are carried out using two power management strategies: optimization and without optimization (i.e., storage priority). The results reveal that the coefficient $\gamma$ reduces the overall energy cost and whatever the applied coefficient, optimization still provides good performances and significantly reduces the global energy cost. Full article

This manuscript aims to study a generalized, set-valued, mixed-ordered, variational inclusion problem involving $\mathcal{H}(·,·)$-compression XOR-${\alpha }_{\mathcal{M}}$-non-ordinary difference mapping and relaxed cocoercive mapping in real-ordered Hilbert spaces. The resolvent operator associated with $\mathcal{H}(·,·)$-compression XOR-${\alpha }_{\mathcal{M}}$-non-ordinary difference mapping is defined, and some of its characteristics are discussed. We prove existence and uniqueness results for the considered generalized, set-valued, mixed-ordered, variational inclusion problem. Further, we put forward a three-step iterative algorithm using a ⊕ operator, and analyze the convergence of the suggested iterative algorithm under some mild assumptions. Finally, we reconfirm the existence and convergence results by an illustrative numerical example. Full article

In this paper, by utilizing the resolvent operator theory, the stochastic analysis method and Picard type iterative technique, we first investigate the existence as well as the uniqueness of mild solutions for a class of $\alpha \in (1,2)$ -order Riemann–Liouville fractional stochastic evolution equations of Sobolev type in abstract spaces. Then the symmetrical technique is used to deal with the $\alpha \in (1,2)$ -order Caputo fractional stochastic evolution equations of Sobolev type in abstract spaces. Two examples are given as applications to the obtained results. Full article

Background: Several natural products have been reported to elicit beneficial effects against neurodegenerative disorders due to their vitamin E contents. However, the neuroprotective efficacy of palm oil or its tocotrienol-rich fraction (TRF) from the pre-clinical cell and animal studies have not been systematically reviewed. Methods: The protocol for this systematic review was registered in “PROSPERO” (CRD42019150408). This review followed the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines. The Medical Subject Heading (MeSH) descriptors of PubMed with Boolean operators were used to construct keywords, including (“Palm Oil”[Mesh]) AND “Nervous System”[Mesh], (“Palm Oil”[Mesh]) AND “Neurodegenerative Diseases”[Mesh], (“Palm Oil”[Mesh]) AND “Brain”[Mesh], and (“Palm Oil”[Mesh]) AND “Cognition”[Mesh], to retrieve the pertinent records from PubMed, Scopus, Web of Science and ScienceDirect from 1990 to 2019, while bibliographies, ProQuest and Google Scholar were searched to ensure a comprehensive identification of relevant articles. Two independent investigators were involved at every stage of the systematic review, while discrepancies were resolved through discussion with a third investigator. Results: All of the 18 included studies in this review (10 animal and eight cell studies) showed that palm oil and TRF enhanced the cognitive performance of healthy animals. In diabetes-induced rats, TRF and α-tocotrienol enhanced cognitive function and exerted antioxidant, anti-apoptotic and anti-inflammatory activities, while in a transgenic Alzheimer’s disease (AD) animal model, TRF enhanced the cognitive function and reduced the deposition of β-amyloid by altering the expression of several genes related to AD and neuroprotection. In cell studies, simultaneous treatment with α-tocotrienols and neurotoxins improved the redox status in neuronal cells better than γ- and δ-tocotrienols. Both pre-treatment and post-treatment with α-tocotrienol relative to oxidative insults were able to enhance the survival of neuronal cells via increased antioxidant responses. Conclusions: Palm oil and its TRF enhanced the cognitive functions of healthy animals, while TRF and α-tocotrienol enhanced the cognitive performance with attenuation of oxidative stress, neuroinflammation and apoptosis in diabetes-induced or transgenic AD animal models. In cell studies, TRF and α-tocotrienol exerted prophylactic neuroprotective effects, while α-tocotrienol exerted therapeutic neuroprotective effects that were superior to those of γ- and δ-tocotrienol isomers. Full article

Mathematical analysis of the well known model of a piezoelectric energy harvester is presented. The harvester is designed as a cantilever Timoshenko beam with piezoelectric layers attached to its top and bottom faces. Thin, perfectly conductive electrodes are covering the top and bottom faces of the piezoelectric layers. These electrodes are connected to a resistive load. The model is governed by a system of three partial differential equations. The first two of them are the equations of the Timoshenko beam model and the third one represents Kirchhoff’s law for the electric circuit. All equations are coupled due to the piezoelectric effect. We represent the system as a single operator evolution equation in the Hilbert state space of the system. The dynamics generator of this evolution equation is a non-selfadjoint matrix differential operator with compact resolvent. The paper has two main results. Both results are explicit asymptotic formulas for eigenvalues of this operator, i.e., the modal analysis for the electrically loaded system is performed. The first set of the asymptotic formulas has remainder terms of the order $O\left(\frac{1}{n}\right)$ , where n is the number of an eigenvalue. These formulas are derived for the model with variable physical parameters. The second set of the asymptotic formulas has remainder terms of the order $O\left(\frac{1}{n^2}\right)$ , and is derived for a less general model with constant parameters. This second set of formulas contains extra term depending on the electromechanical parameters of the model. It is shown that the spectrum asymptotically splits into two disjoint subsets, which we call the $\alpha$ -branch eigenvalues and the $\theta$ -branch eigenvalues. These eigenvalues being multiplied by “i” produce the set of the vibrational modes of the system. The $\alpha$ -branch vibrational modes are asymptotically located on certain vertical line in the left half of the complex plane and the $\theta$ -branch is asymptotically close to the imaginary axis. By having such spectral and asymptotic results, one can derive the asymptotic representation for the mode shapes and for voltage output. Asymptotics of vibrational modes and mode shapes is instrumental in the analysis of control problems for the harvester. Full article