Rıemann-Lıouvılle kesirli türev ile eğrilerin geometrisi
Küçük Resim Yok
Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Trakya Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tez çalışmasında Riemann-Liouville kesirli türev operatörü yardımıyla ?^2 ve ?^3 uzayında eğrilerin diferansiyel geometrisi çalışılmıştır. Riemann-Liouville kesirli türevine göre eğrinin teğet, normal ve binormal vektörleri bulunarak, eğrilik ve burulması hesaplanmıştır. Klasik türev ve kesirli türev arasındaki ilişki ortaya konularak, kesirli türev ile eğrilerin incelemesi yapılıp, yeni tanım ve teoremler verilmiştir.
In this thesis, differential geometry of curves in ?^2 and ?^3 space was studied with the help of the Riemann-Liouville fractional derivative operator. According to the Riemann-Liouville fractional derivative, the tangent, normal and binormal vectors of the curve were found and its curvature and torsion were calculated. The relationship between classical derivative and fractional derivative is revealed, fractional derivative and curves are examined, and new definitions and theorems are given.
In this thesis, differential geometry of curves in ?^2 and ?^3 space was studied with the help of the Riemann-Liouville fractional derivative operator. According to the Riemann-Liouville fractional derivative, the tangent, normal and binormal vectors of the curve were found and its curvature and torsion were calculated. The relationship between classical derivative and fractional derivative is revealed, fractional derivative and curves are examined, and new definitions and theorems are given.
Açıklama
Yüksek Lisans
Anahtar Kelimeler
Matematik, Mathematics
