On a Fractional Operator of Adjoint Hybrid Fractional Derivative Operator

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Atıf İçin Kopyala

BAYRAK M. A., DEMİR A.

Annals of the University of Craiova, Mathematics and Computer Science Series, cilt.51, sa.1, ss.21-39, 2024 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 51 Sayı: 1
• Basım Tarihi: 2024
• Doi Numarası: 10.52846/ami.v51i1.1678
• Dergi Adı: Annals of the University of Craiova, Mathematics and Computer Science Series
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
• Sayfa Sayıları: ss.21-39
• Anahtar Kelimeler: Caputo Fractional derivative, Homotopy analysis method, Time fractional initial value problem
• Kocaeli Üniversitesi Adresli: Evet

Özet

The achievement of this paper is to propose a new kind of fractional derivative which is called New Constant Proportional Caputo (NCPC) operator and to construct the solution of time-fractional initial value problem (TFIVPs) with NCPC derivative by taking the combination of Laplace transform (LT) and Homotopy Analysis method (HAM) into account. Later, the obtained solution is compared with the solutions of TFIVPs with Caputo and Constant Proportional Caputo (CPC) derivatives. The gained results reveal that the combination of LT and HAM together form an efficient method to build the approximate results of TFIVPs in NCPC sense.