Sesamum alatum Thonn. (Introduced) (Angola, Benin, Botswana, Burkina, Cameroon, Caprivi Strip, Chad, Egypt, Eritrea, Ethiopia, Ghana, Guinea, India (I), Kenya, KwaZulu-Natal, Mali, Mauritania, Mozambique, Namibia, Niger, Nigeria, Northern Provinces, Senegal, Sudan, Swaziland, Western Sahara, Zambia, Zimbabwe; Introduced in  as per POWO)

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Sesamum indicum L. (Native to Assam, Bangladesh, India, Lebanon-Syria, West Himalaya; Introduced to Afghanistan, Alabama, Andaman Is., Angola, Belize, Benin, Bolivia, Borneo, Brazil North, Bulgaria, Burkina, Burundi, California, Cambodia, Cameroon, Central African Repu, Chad, China South-Central, China Southeast, Congo, Costa Rica, Cuba, Cyprus, East Himalaya, Egypt, El Salvador, Eritrea, Ethiopia, Fiji, Florida, French Guiana, Gabon, Galápagos, Gambia, Georgia, Ghana, Greece, Guatemala, Guinea, Guinea-Bissau, Guyana, Hainan, Honduras, Iran, Ivory Coast, Japan, Kazakhstan, Kenya, Korea, Krym, KwaZulu-Natal, Laos, Lesser Sunda Is., Liberia, Libya, Louisiana, Madagascar, Malawi, Malaya, Mali, Masachusettes, Mauritania, Mauritius, Mexico Gulf, Mexico Southwest, Missouri, Morocco, Mozambique, Myanmar, Nepal, New Jersey, New York, Nicobar Is., Niger, Nigeria, Northern Provinces, Ohio, Pakistan, Pennsylvania, Peru, Philippines, Rwanda, Saudi Arabia, Senegal, Sierra Leone, Somalia, South Carolina, South European Russi, Spain, Sri Lanka, Sudan, Suriname, Swaziland, Tadzhikistan, Tanzania, Texas, Thailand, Togo, Transcaucasus, Trinidad-Tobago, Turkey, Turkey-in-Europe, Uganda, Ukraine, Uzbekistan, Venezuela, Vietnam, Wisconsin, Yemen, Yugoslavia, Zambia, Zaïre, Zimbabwe as per POWO)
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Sesamum prostratum Retz. (S-India, Sri Lanka)

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Systematics and evolution in Sesamum L. (Pedaliaceae), part 1: Evidence regarding the origin of sesame and its closest relativesDorothea Bedigian- Webbia 70(1):1-42 · January 2015:
(Abstract: Morphologically leaves of both look quite different. But in view of the paper you stated I have to merge both as per abstract:
Recent molecular studies demonstrate that Sesamum sect. Sesamum, defining the largest genus of Pedaliaceae, holds two subspecies: the oilseed crop Sesamum indicum, and the crop’s progenitor Sesamum indicum subsp. malabaricum, and fail to support the idea that cultivated sesame originated from the African Sesamum latifolium. Therefore, in this updated classification, Sesamum sect. Sesamum is re-circumscribed to contain the Asian progenitor species of sesame. As a result, these data do not support the current infrageneric classification system; instead, these molecular results offer alternative implications with regard to the evolution of the genus and provide a basis for developing an updated taxonomy that is consistent with underlying phylogenetic relationships. Each clade is recognized as a section, thereby retaining valuable information on evolutionary relationships while minimizing nomenclatural changes. These analyses also reveal that section Sesamum is sister to Sesamum sect. Chamaesesamum. That section holds two species, Sesamum laciniatum and Sesamum prostratum, that have frequently been treated as distinct, but are combined here).
Key to the subspecies of Sesamum indicum L.
1. Plant generally 25–110 cm high, branched or unbranched, depending on cultivar. Living plant colour yellow-green, fern green, shamrock green, emerald
green, forest green, jade green, sea green or dark green with purplish hue. Lower leaves vary according to cultivar – occasionally divided (Figure 5), tripartite, with toothed margins (Figure 6), some with leafy outgrowths at base of leaves above petiole (Figure 7); many cultivars with lanceolate, or simple ovate leaves and entire margins (Figure 7). Upper leaves (bracts) linear with entire margins (Figure 7). Corolla 15–33 mm long, violet, pink or white; length of lower lobe equal to, or 2–10 mm longer than other lobes, depending on cultivar; colour variable, white, light pink, pale lavender to deep purple, or with pale lavender lines, pigmentation throughout the lower lobe or along the margin only; exterior and interior coloration ranges on scale 1–10, from 1–8, in line with cultivar; some with linear markings, some tinted only at lower margin of lower lip, of variable intensity and amount of surface area covered. Extrafloral nectaries 1–1.2 mm in diameter. Capsule 15–50 mm by 6–14 mm; bicarpellate (Figures 8–10) or tetracarpellate (Figures 11, 12), texture papery to woody (variable). Seeds 1.5–4 mm long; colour variable – white, ivory, beige, tan, mustard yellow, brick red, various shades of brown, grey or black; egg- to teardrop-shaped, surfaces smooth or granular, seldom transversely or reticulately rugose, with edges sloping; seeds not dormant ………. 1. subsp. indicum        
2. Plant often reaches 200 cm high, typically branching profusely. Living plant colour dark green, often with purplish hue. Lower leaves divided, in less developed leaves undivided, margins serrate, without leafy outgrowths at base of leaves above petiole. Upper leaves cordate. Corolla 22–55 mm long, generally white to pale purple; lower lip 10–15 mm long, and dark purple, the colour ranking 10, on a scale 1–10, and occupying entire lower lip. Extrafloral nectaries 2– 3 mm in diameter. Capsule 20–25 mm by 6 mm; only bicarpellate, woody. Seeds 2–2.5 mm long; colour dark brown or black, broadly ovate, surfaces conspicuously reticulately rugose, with distinct sharp edges, sides broad, all sides conspicuously transversely or reticulately rugose; seeds markedly dormant ……………… 2. subsp. malabaricum (Not accepted as per Flora of North America Editorial Committee (2019). Flora of North America North of Mexico 17: 1-737. Oxford University Press, New York, Oxford as per POWO)

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A New Combination for the Indian Progenitor of Sesame, Sesamum indicum (Pedaliaceae)– Dorothea Bedigian- Novon Vol. 23, No. 1 (April 2014)pp. 5-13:
(Abstract: The new combination Sesamum indicum L. subsp. malabaricum (Burm.) Bedigian (Pedaliaceae) is provided for the progenitor of sesame. Both lectotype and epitype for S. malabaricum Burm., the basionym of the new combination, are designated herein. A plate (van Rheede tot Draakestein, 1689: tab. 55) mentioned in the original protologue (Burman,1769) is designated here as the lectotype for S.indicum L. subsp. malabaricum (Burm.) Bedigian. Previously published evidence about the relationship of S. indicum and S. malabaricum summarized here
and shared morphological traits described here provide a foundation for the recognition of this taxon at the changed rank of subspecies)

KEY TO THE SUBSPECIES OF SESAMUM INDICUM L.
1a. Seed color variable, white, ivory, beige, tan, mustard yellow, brick red, various shades of brown, gray, or black; seed surfaces smooth, granular, seldom transversely or reticulately rugose, not dormant; corolla 15–33 mm long; lower lip occasionally equal to, or more usually 2–10 mm longer than, other lobes; corolla coloration variable, from white, light pink, pale lavender to light purple, or with pale lavender lines, ranging in intensity from 1 to 8 on a scale of 1 to 10, coloration varies with cultivar, some with linear markings, some tinted only at lower margin of lower lip, with variable intensity and variable amount of surface area covered; capsule 1.5–5 cm long, bicarpellate and tetracarpellate, texture papery to woody (variable); living plant color in shades of green, extending from yellow green, fern green, shamrock green, emerald green, forest green, jade green, sea green, dark green with purplish hue; extrafloral nectary glands 1–1.2 mm; plant generally 30–110 cm high, branching variable, cultivar-dependent, from single-stemmed to profusely branching; lower leaves varying by cultivar, ranging from occasionally divided, tripartite, with toothed margins, some with leafy outgrowths at base of leaves above petiole; many cultivars with
lanceolate or simple ovate leaves . . . . . . S. indicum subsp. indicum
1b. Seed color dark brown or black; seed surface conspicuously reticulate and rugose, markedly dormant; seeds 2–2.5 mm long, with distinct sharp edges, sides broad, transversely or reticulately rugose; corolla 22.5–55 mm long; lower lip 10–15 mm longer than other lobes, dark purple, with intensity of color ranking 10 on a scale of 1 to 10, pigmentation occupying entire lower lip; capsule 2–2.5 cm long, bicarpellate, texture woody; living plant color dark green, often with purplish hue; extrafloral nectary glands 2–3 mm; plant often reaching 200 cm high, typically branching profusely; lower leaves divided, undivided, and serrate in less-developed leaves, without leafy outgrowths at base of leaves above petiole  . . . . . . . S. indicum subsp. malabaricum (Not accepted as per Flora of North America Editorial Committee (2019). Flora of North America North of Mexico 17: 1-737. Oxford University Press, New York, Oxford as per POWO)


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Flora of Eastern Karnataka, Volume 2  By N. P. Singh (1988)- Descriptions of
Sesamum laciniatum (syn. of Sesamum prostratum)
Sesamum orientale L. is a synonym of Sesamum indicum L.)

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BINOMIAL HABIT NOTES REFERENCES DISTRIBUTION
Sesamum
alatum
Thonn.
Herb Sandy Coast,  Naturalized, Native of Africa Flora of Tamil Nadu, VOL. II,
1987
Cuddalore, Kanchee puram,
Thiruvallur, Viluppuram 
Sesamum
indicum
L.
Herb Plains, Cultivated Flora of Tamil Nadu, VOL. II,
1987
All districts
Sesamum
laciniatum
Klein ex Willd. (syn. of Sesamum prostratum)
Herb Plains to Low Altitude, Dry
Localities
Flora of Tamil Nadu, VOL. II,
1987; Matthew 1983
Coimbatore, Dharmapuri,
Pudduk kottai, Salem, Tiruchchira ppalli
Sesamum
prostratum
Retz.
Herb Plains, Sandy soils  Flora of Tamil Nadu, VOL. II,
1987
Coimbatore, Cuddalore,
Kanchee puram, Thanjavur, Thiruvallur, Tiruchchira ppalli, Viluppuram
Sesamum
radiatum
Schumach. & Thonn.
Herb Low elevations,  Naturalized,  Native of Africa Matthew, 1999 Dindigul


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Descriptors for Sesame (Sesamum spp.) By Bioversity (2004)- Details- 
Sesamum laciniatum (syn. of Sesamum prostratum)
Sesamum malabaricum Burm. (syn. of Sesamum indicum)
Sesamum prostratum

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Flora of Guntur District, Andhra Pradesh, India (1998)- Details with keys–