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The concept of convexity of functions is a useful instrument that is used to solve a wide range of pure and applied scientific issues. The Hermite-Hadamard inequality which is also used frequently in many other parts of practical mathematics notably in optimization and probability is one of the most important mathematical inequalities relevant to convex maps. The fractional calculus, a calculus of non-integer order has applications in diverse fields of physical sciences. In this paper, we have established Hermite-Hadamard's inequalities via Riemann-Liouville fractional integral for the case of harmonically convex function as well as the products of two harmonically convex functions via Riemann-Liouville fractional integrals. [ABSTRACT FROM AUTHOR]

Simple Summary: Wetlands of mid-hills and lesser Himalaya in Nepal are highly threatened due to climate change and human encroachment. This study assessed the change in total surface coverage of water bodies in the Ramaroshan Wetland Complex of western Nepal over the last three decades and explored the diversity and environmental determinants of the resident herpetofauna by line transect sampling during September/October 2021. The wetland complex is threatened by a net loss of 16% in water coverage over the last three decades. Eleven species of herpetofauna (five amphibians and six reptiles) within five families of two orders were recorded in the study area. The area has low herpetofaunal diversity that indicates poor ecosystem health of the wetland complex. Therefore, we recommend immediate conservation and restoration initiatives to ensure the sustainability of the wetland. Wetlands are among the highly threatened ecosystems due to anthropogenic activities. The Ramaroshan Wetland Complex (RWC) of Achham District, Nepal is one of the high-altitude wetlands facing human induced degradation and loss. Herpetofauna are key bio-indicators of environmental health and habitat quality and are useful to assess habitat conditions of such threatened ecosystems. This study quantified the land use and land cover (LULC) change in the RWC and documented the diversity and distribution pattern of herpetofauna. The LULC in the area (13.94 Km2) was analyzed for 1989, 2000, 2010 and 2021 by supervised classification of remote sensing images. Surveys were conducted along 25 transects, each of 200 m in length and environmental variables were recorded for every observation of herpetofauna. The LULC analysis revealed an overall loss of 16% of the total water body between 1989 (0.25 Km2) and 2021 (0.21 Km2). Eleven species of herpetofauna (five amphibians and six reptiles) within five families and two orders (i.e., Anura and Squamata), were recorded with low diversity (H' = 1.88312) and evenness (E = 0.3642) indices. The herpetofauna had a hump-shaped distribution along the elevation gradient with the highest richness and abundance at 2300 m asl. Amphibian abundance decreased with increasing distance to nearest water sources, whereas reptile abundance increased. Amphibians were more abundant in agricultural field and marsh land, whereas reptile abundance was higher around human settlements. Results indicate that the wetland area in the RWC is declining at an alarming rate and, in turn, might account for the low diversity and abundance of the herpetofauna. [ABSTRACT FROM AUTHOR]