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The Lord Shulman swelling porous thermo-elastic soil system with the effects of microtemperature, temperatures and distributed delay terms is considered in this study. The well-posedness result is established by the Lumer–Phillips corollary applied to the Hille–Yosida theorem. The exponential stability result is proven by the energy method under suitable assumptions. [ABSTRACT FROM AUTHOR]

In this work, by the use of a semigroup theory approach, we provide a global solution for an initial boundary value problem of the wave equation with logarithmic nonlinear source terms and fractional boundary dissipation. In addition to this, we establish a blow-up result for the solution under the condition of non-positive initial energy. [ABSTRACT FROM AUTHOR]

In this research, we investigate the presence of weak positive solutions for a family of anisotropic non-local elliptic systems in bounded domains using the sub-super solutions approach in conjunction with Schauder's fixed point. [ABSTRACT FROM AUTHOR]

Positivity analysis is used with some basic conditions to analyse monotonicity across all discrete fractional disciplines. This article addresses the monotonicity of the discrete nabla fractional differences of the Riemann–Liouville type by considering the positivity of ∇ b 0 R L θ g (z) combined with a condition on g (b 0 + 2) , g (b 0 + 3) and g (b 0 + 4) , successively. The article ends with a relationship between the discrete nabla fractional and integer differences of the Riemann–Liouville type, which serves to show the monotonicity of the discrete fractional difference ∇ b 0 R L θ g (z) . [ABSTRACT FROM AUTHOR]

This paper explores the time dependent squeezing flow of a viscous fluid between parallel plates with internal heat generation and homogeneous/heterogeneous reactions. The motive of the present effort is to upgrade the heat transformation rate for engineering and industrial purpose with the rate of chemical reaction. For this purpose the equations for the conservation of mass, momentum, energy and homogeneous/heterogeneous reactions are transformed to a system of coupled equations using the similarity transformation. According to HAM, with the proper starting assumptions and other factors, a similarity solution may be found. On the way to verifying the validity and correctness of HAM findings, we compare the HAM solution with numerical solver programme BVP4c to see whether it matches up. The results of a parametric inquiry are summarized and presented with the use of graphs. [ABSTRACT FROM AUTHOR]