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This paper delves into an examination of the existence, uniqueness, and stability properties of a non-local integro-differential equation featuring the Hilfer fractional derivative with order ω∈(1,2) for the RLC model. Based on Schaefer’s fixed point theorem and Banach’s contraction principle, the existence and uniqueness results are established. Furthermore, Ulam–Hyers and Ulam–Hyers–Rassias stability results for the boundary value problem of the RLC model are discussed. To showcase the practicality and efficacy of our theoretical findings, a two-step Lagrange polynomial interpolation method is applied to solve some numerical examples.

Summary In this paper, computational analysis of a Caputo fractional variable‐order system with inductor‐capacitor (LC) and resistor‐capacitor (RC) electrical circuit models is presented. The existence and uniqueness of solutions to the given problem are determined using Schaefer's fixed point theorem and the Banach contraction principle, respectively. The proposed problem's computational consequences are addressed and analyzed using modified Euler and Runge–Kutta fourth‐order techniques. Furthermore, the suggested model compares several orders, including integer, fractional, and variable orders. To demonstrate the utility of the proposed approach, computational simulations are carried out on LC and RC circuit models of various orders. Furthermore, a comparative analysis with previous investigations has been carried. For the given problem, the numerical solution results in high‐precision approximations. [ABSTRACT FROM AUTHOR]

Clonostachys rosea, an ascomycetous, omnipresent, cellulose-decaying soil fungus, has been reported to be a well-known mycoparasitic biological control agent. In this study, we isolated C. rosea, a mycoparasitic fungus for the first time in India from sclerotia of the notorious plant pathogen Sclerotinia sclerotiorum, causing head rot disease in cabbage. A total of five mycoparasitic fungi were isolated from the sclerotial bodies of S. sclerotiorum (TNAU-CR 01, 02, 03, 04 and 05). All the isolates were tested under morpho-molecular characterization. Among them, TNAU-CR 02 showed the greatest mycelial inhibition of 79.63% over the control. Similarly, the SEM imaging of effective C. rosea isolates indicated the presence of numerous conidia destroying the outer cortex layers of sclerotia. Metabolite fingerprinting of C. rosea TNAU-CR 02 identified 18 chemical compounds using GC-MS analysis. The crude antibiotics of C. rosea TNAU-CR 02 were verified for their antifungal activity against S. sclerotiorum and the results revealed 97.17% mycelial inhibition compared with the control. Similarly, foliar application of TNAU-CR 02 at 5 mL/litre on 30, 45 and 60 days after transplanting showed the lowest disease incidence of 15.1 PDI compared to the control. This discovery expands our understanding of the biology and the dissemination of C. rosea, providing a way for the exploitation of C. rosea against cabbage head rot pathogens.

This paper presents the computational analysis of fractional differential equations of variable‐order delay systems. To the proposed problem, the existence of solutions is derived using Arzela‐Ascoli theorem, and the Banach fixed point theorem is used for uniqueness results. To investigate and address the computational solutions, Adams‐Bashforth‐Moulton technique is established. To demonstrate the method's efficiency, computational simulations of chaotic behaviors in several one‐dimensional delayed systems with distinct variable orders are employed. The numerical solution of the proposed problem gives high precision approximations. [ABSTRACT FROM AUTHOR]