THE NEW SUMUDU TRANSFORM ITERATIVE METHOD FOR STUDYING THE RANDOM COMPONENT TIME-FRACTIONAL KLEIN-GORDON EQUATION

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Atıf İçin Kopyala

MERDAN M., Anac H., KESEMEN T.

SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, cilt.10, sa.3, ss.343-354, 2019 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 10 Sayı: 3
• Basım Tarihi: 2019
• Dergi Adı: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Academic Search Premier, Directory of Open Access Journals
• Sayfa Sayıları: ss.343-354
• Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

In this study, the solutions of the random component time-fractional Klein-Gordon equation is obtained as approximately or exactly. The initial condition of this Klein-Gordon equation is studied by Gamma distribution. The fractional derivatives are defined in the Caputo sense. An example is shown to illustrate the influence of the solutions obtained by the new Sumudu transform iterative method (NSTIM). The expected value and variance of these solutions of this Klein-Gordon equation are obtained. The approximate analytical solution of this equation obtained by NSTIM and VIM are compared. NSTIM is applied to analyze the solution of this equation. Solution and figures are obtained by using MAPLE software. The formulas for the expected values and variances and results from the simulations of this Klein-Gordon equation are compared and the efficiency of this method is investigated.