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In this research, we present a novel and computationally streamlined method to tackle nonlocal initial value problems through a combination of modeling and simulation. Our approach utilizes the Integro spline quasi-interpolation technique, renowned for its effectiveness in approximating nonlocal integrals. To validate the efficacy of our proposed method, we conduct comprehensive comparisons with alternative approaches found in the existing literature for integrating nonlocal functions. Additionally, we successfully apply our suggested approach to address nonlocal Riccati, resistor-inductor circuit, and Airy oscillator dynamical systems. The numerical results obtained from these applications convincingly demonstrate the advantages and effectiveness of our developed approach in enhancing mathematical simulation. [ABSTRACT FROM AUTHOR]

This paper presents an innovative and efficient method for solving the fractional-order Van der Pol impulsive system. In particular, the proposed scheme utilizes finite difference techniques for approximating fractional integrals, and its efficacy is compared to existing integration methods presented in the literature. Moreover, the proposed approach is applied to fractional impulsive systems, specifically the Fractional Van der Pol system with impulse behavior. The results demonstrate the effectiveness of the impulsive treatment effects for the system under consideration. In general, this study offers an insightful contribution to the field of fractional calculus, while providing a practical and efficient solution for solving impulsive systems. [ABSTRACT FROM AUTHOR]

This paper proposes an effective numerical scheme for solving impulsive fractional differential equations. For this purpose, Hermite interpolation is used to approximate fractional-order integrals. The proposed methods convergence analysis is studied in detail by bounding the approximation error. Finally, the application and performance of the presented method are illustrated in two practical examples, including the impulsive control of the family of Lorenz systems, and the obtained results are compared with an existing method. [ABSTRACT FROM AUTHOR]

In many countries, a rail network consists of single lines with sidings where interactions between trains occur (meet, pass). In this paper, we study two issues of these networks: first, the scheduling of freight trains in a single-line corridor while ensuring safe interactions and second, the allocation of freight-to-freight trains regarding the release dates of freight, weight of freight, and weight capacity of the trains. Both of these issues must be addressed when examining real-world freight train scheduling problems. The objective functions of this study are the minimization of a train's travelling time, the allocation of freight-to-freight trains, and the reduction of tardiness of freight at destination. Both scheduling and allocation problems are presented using integer linear programming models. In addition, an integrated novel heuristic algorithm has been proposed to solve them. Computational results demonstrated through a generated dataset show both model validation and efficiency of the heuristic algorithm. The heuristic algorithm has been designed to incorporate the practical operational railway rules with modest modification. Although its outputs slightly differ from the exact solutions, it can solve both models simultaneously in large-scale problems. [ABSTRACT FROM AUTHOR]

Dynamical systems with delay are widespread in nature. The study of time-delay induced changes in the collective behavior of systems of coupled nonlinear oscillators is a subject of great interest, both because of its fundamental importance from the point of view of dynamical systems and because of its practical applications. In this paper, an explicit technique is proposed for numerical solution of nonlocal dynamical systems with time delay. The proposed method is adopted quadratic spline interpolation. Then, the error analysis of the developed method is discussed. It is exploited in the discussion of nonlocal delay Ikeda and Hutchinson models. Finally, the performance of the presented approach is verified by applying the error and convergence study for different values of fractional order parameters. [ABSTRACT FROM AUTHOR]

Dermatomyositis (DM) is a rare inflammatory myopathy with an incidence of 9.63 per 1 000 000 people and typically presents with skin rash and muscle weakness. We report a case of DM that presented with proximal muscle weakness, normal creatine phosphokinase (CPK), negative myositis antibody panel, and non-specific histopathological findings on muscle biopsy, without initial skin involvement. A 67-year-old male presented with subacute bilateral proximal lower-extremity weakness and weight loss of 20 pounds over 3 months. Laboratory investigation was significant for elevated erythrocyte sedimentation rate, C-reactive protein, CPK, and aldolase, with negative myositis-specific antibodies. Femur magnetic resonance imaging revealed subcutaneous, fascial, and muscle edema throughout quadriceps and gluteal muscles. Muscle biopsy showed myofiber atrophy with perivascular and endomysial T-lymphocytes and histiocytes, as well as scattered necrotic myofibers. He was diagnosed with inflammatory myositis and started on prednisone and monthly IVIG infusions. At 2-month follow-up, he reported new rashes on the extensor surfaces of the hands consistent with Gottron’s papules, mechanic’s hands, and livedo reticularis of feet and arms. Cases of DM that present with myopathy and later develop skin changes are rare. Our patient had several months of progressive proximal muscle weakness, and skin changes occurred after he was started on treatment. Laboratory findings include elevated CPK, aldolase, and myositis-specific auto-antibodies. Muscle biopsy helps in diagnosis; however, findings may be nonspecific—as was the case in our patient. Corticosteroids are first-line treatment. Long-term follow-up studies are necessary to better understand the incidence of late-onset development of typical skin findings.

In this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is defined. The existence and uniqueness theorem for the interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examples show the effectiveness and efficiency of the approach. [ABSTRACT FROM AUTHOR]