Araştırma Makalesi
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Cauchy Problem for Fractional Order Second Type Volterra Equation

Yıl 2020, Cilt: 3 Sayı: 2, 33 - 39, 30.12.2020

Öz

The presence of different definitions of derivatives in the mathematical analysis of fractional order allows you to get the best solution in accordance with the definition of various scientific and technical problems. Therefore, interest in the use of fractional-order differential equations in problems of mathematical modeling is progressively increasing. In this study, in the continuous and integrable space of functions B_(p,θ)^() (G,s) -Dzhabrailov-Alisoy, we study a Cauchy-type problem for D_a^ν y(x)=f[x,y(x)]-differential equations of fractional order on a G⊂R

Kaynakça

  • [1] M. Caputo, Elasticita e Dissipazione. Italy: Zanichelli and Bologna, 1969.
  • [2] K.B. Oldham and J. Spanier, The Fractional Calculus. New York: Academic Press,1974.
  • [3] Babenko, Yu.I., Teplomassoobmen. Metod rascheta teplovykh i diffuzionnykh potokov (Heat and Mass Transfer: Method for Calculating Heat and Diffusion Fluxes), Leningrad: Khimiya, 1986. (in Russian)
  • [4] S.G. Samko, A.A. Kilbas and 0.1. Marichev, Fractional Integrals and Derivatives.Theory and Appiications, Gordon and Breach, Yerdon, 1993
  • [5] K.S. Miller and B. Ross, An İntroduction to the Fractional Calculus and Differential Equations. New York: Jhon Willy and Sons, 1993.
  • [6] V. Kiryakova, Generalized Fractional Calculus and Applications. Long-man & J. Wiley,Harlow & N. York (1994)
  • [7] J.J. Distefano, A.R. Stubberud and I.J. Williams, Theory and Problems of Feedback and Control Systems. New York: McGraw-Hill, 1995.
  • [8] A. Carpintery and F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics. New York: CSIM Courses and Lectures, 1997.
  • [9] I. Podlubny, Fractional Differential Equations. New York: Academic Press, 1999.
  • [10] A.A. Kilbas, N.M. Srivastavo and J.J. Tzujillo, Theory and Applications of Fractonal Differential Equations. Amsterdam: Elsever, 2006.
  • [11] Kholpanov, L.P. and Zakiev, S.E.,(2005) Fractional IntegroDifferential Analysis of Heat and Mass Transfer, Inzh.-Fiz.Zh.,78(1),35
  • [12] Ayazoglu, R., Saraç, Y., Şener, S. and Alisoy G.,(2020) Existence and multiplicity of solutions for a SchrödingerKirchhof type equation involving the fractional p(.,.)-Laplacian operator in Rn, Collect.Math.
  • [13] A. Ates, B.B. Alagoz, G.T. Alisoy, C Yeroglu and H.Z. Alisoy.,(2015), Fuzzy Velocity and Fuzzy Acceleration in Fractional Order Motion, Balkan Journal of Electrical & Computer Engineering, 3 (2), 98-102
  • [14] Alagoz, B.B., Alisoy, G., Alagoz, S., Alisoy, H. (2017). A note on applications of time-domain solution of Cole permittivity models. Optik, 139, 272-282.
  • [15] Kerimova (Alisoy) G.T. (1997), “Properties of differential functions with repeated difference- differential characteristic depending on multi-package variables” PhD Thesis , Baku,p127. (in Russian)
  • [16] Maksudov F.T., Dzhabrailov A.D.,(2000),The method of integral representations in the theory of spaces,V.1 Baku – “Elm”, p.200 (in Russian)
  • [17] Alisoy G.T, Alisoy H.Z., (2002),On integral representations of multi package variable functions, International Journal of Applied Mathematics, 11, 371-386.
  • [18] Alisoy G.T, Dzhabrailov A.D. , Alisoy H.Z, (2005), Properties of functions in some weighted spaces, Applicable Analysis, 84, 405-417.
  • [19] Gülizar ALİSOY, Sadiye AKTAŞ, (2018), Diferansiyel Fark Özelliklerinin Korunması ile Çok Katlı Değişkenlere Bağımlı Fonksiyonların G⊂E^n Bölgesi Dışına Genişletilmesi, Mus Alparslan University Journal of Science, 6(1), 493-500.

Kesirli Mertebe İkinci Çeşit Volterra Denklemi İçin Cauchy Problemi

Yıl 2020, Cilt: 3 Sayı: 2, 33 - 39, 30.12.2020

Öz

Kesirli mertebe matematik analizde farklı türev tanımlarının varlığı, değişik fen ve mühendislik problemlerinin tanımlanma biçimine uygun olarak en iyi çözümünün elde edilmesine olanak sağlamaktadır. Bu nedenle, matematiksel modelleme problemlerinde kesirli mertebe diferintegral denklemlerin kullanımına olan ilgi giderek artmaktadır. Bu çalışmada, sürekli ve integrallenebilir fonksiyonların B_(p,θ)^()(G,s)-Dzhabrailov-Alisoy uzayında, G⊂R olmak üzere, D_a^ν y(x)=f[x,y(x)]- kesirli mertebeden diferansiyel denklemler için bir Cauchy tipi problem incelenmiştir.

Kaynakça

  • [1] M. Caputo, Elasticita e Dissipazione. Italy: Zanichelli and Bologna, 1969.
  • [2] K.B. Oldham and J. Spanier, The Fractional Calculus. New York: Academic Press,1974.
  • [3] Babenko, Yu.I., Teplomassoobmen. Metod rascheta teplovykh i diffuzionnykh potokov (Heat and Mass Transfer: Method for Calculating Heat and Diffusion Fluxes), Leningrad: Khimiya, 1986. (in Russian)
  • [4] S.G. Samko, A.A. Kilbas and 0.1. Marichev, Fractional Integrals and Derivatives.Theory and Appiications, Gordon and Breach, Yerdon, 1993
  • [5] K.S. Miller and B. Ross, An İntroduction to the Fractional Calculus and Differential Equations. New York: Jhon Willy and Sons, 1993.
  • [6] V. Kiryakova, Generalized Fractional Calculus and Applications. Long-man & J. Wiley,Harlow & N. York (1994)
  • [7] J.J. Distefano, A.R. Stubberud and I.J. Williams, Theory and Problems of Feedback and Control Systems. New York: McGraw-Hill, 1995.
  • [8] A. Carpintery and F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics. New York: CSIM Courses and Lectures, 1997.
  • [9] I. Podlubny, Fractional Differential Equations. New York: Academic Press, 1999.
  • [10] A.A. Kilbas, N.M. Srivastavo and J.J. Tzujillo, Theory and Applications of Fractonal Differential Equations. Amsterdam: Elsever, 2006.
  • [11] Kholpanov, L.P. and Zakiev, S.E.,(2005) Fractional IntegroDifferential Analysis of Heat and Mass Transfer, Inzh.-Fiz.Zh.,78(1),35
  • [12] Ayazoglu, R., Saraç, Y., Şener, S. and Alisoy G.,(2020) Existence and multiplicity of solutions for a SchrödingerKirchhof type equation involving the fractional p(.,.)-Laplacian operator in Rn, Collect.Math.
  • [13] A. Ates, B.B. Alagoz, G.T. Alisoy, C Yeroglu and H.Z. Alisoy.,(2015), Fuzzy Velocity and Fuzzy Acceleration in Fractional Order Motion, Balkan Journal of Electrical & Computer Engineering, 3 (2), 98-102
  • [14] Alagoz, B.B., Alisoy, G., Alagoz, S., Alisoy, H. (2017). A note on applications of time-domain solution of Cole permittivity models. Optik, 139, 272-282.
  • [15] Kerimova (Alisoy) G.T. (1997), “Properties of differential functions with repeated difference- differential characteristic depending on multi-package variables” PhD Thesis , Baku,p127. (in Russian)
  • [16] Maksudov F.T., Dzhabrailov A.D.,(2000),The method of integral representations in the theory of spaces,V.1 Baku – “Elm”, p.200 (in Russian)
  • [17] Alisoy G.T, Alisoy H.Z., (2002),On integral representations of multi package variable functions, International Journal of Applied Mathematics, 11, 371-386.
  • [18] Alisoy G.T, Dzhabrailov A.D. , Alisoy H.Z, (2005), Properties of functions in some weighted spaces, Applicable Analysis, 84, 405-417.
  • [19] Gülizar ALİSOY, Sadiye AKTAŞ, (2018), Diferansiyel Fark Özelliklerinin Korunması ile Çok Katlı Değişkenlere Bağımlı Fonksiyonların G⊂E^n Bölgesi Dışına Genişletilmesi, Mus Alparslan University Journal of Science, 6(1), 493-500.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Araştırma Makaleleri
Yazarlar

Gülizar Alisoy

Gözde Arslantaş 0000-0002-7404-2241

Yayımlanma Tarihi 30 Aralık 2020
Gönderilme Tarihi 19 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 2