دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,436
تعداد مقالات17,702
تعداد مشاهده مقاله57,799,312
تعداد دریافت فایل اصل مقاله19,443,355
Jafari, Mohammad, Dastmalchi Saei, Farhad, Jodayree Akbarfam, Ali Asghar, Jahangiri Rad, Mohammad. (1401). The generalized conformable derivative for 4α-order Sturm-Liouville problems. سامانه مدیریت نشریات علمی, 10(3), 816-825. doi: 10.22034/cmde.2021.45363.1908
Mohammad Jafari; Farhad Dastmalchi Saei; Ali Asghar Jodayree Akbarfam; Mohammad Jahangiri Rad. "The generalized conformable derivative for 4α-order Sturm-Liouville problems". سامانه مدیریت نشریات علمی, 10, 3, 1401, 816-825. doi: 10.22034/cmde.2021.45363.1908
Jafari, Mohammad, Dastmalchi Saei, Farhad, Jodayree Akbarfam, Ali Asghar, Jahangiri Rad, Mohammad. (1401). 'The generalized conformable derivative for 4α-order Sturm-Liouville problems', سامانه مدیریت نشریات علمی, 10(3), pp. 816-825. doi: 10.22034/cmde.2021.45363.1908
Jafari, Mohammad, Dastmalchi Saei, Farhad, Jodayree Akbarfam, Ali Asghar, Jahangiri Rad, Mohammad. The generalized conformable derivative for 4α-order Sturm-Liouville problems. سامانه مدیریت نشریات علمی, 1401; 10(3): 816-825. doi: 10.22034/cmde.2021.45363.1908

The generalized conformable derivative for 4α-order Sturm-Liouville problems

Computational Methods for Differential Equations
مقاله 19، دوره 10، شماره 3، مهر 2022، صفحه 816-825    اصل مقاله (416.76 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.45363.1908
نویسندگان
Mohammad Jafari1، 2؛ Farhad Dastmalchi Saei* 1؛ Ali Asghar Jodayree Akbarfam3؛ Mohammad Jahangiri Rad1
1Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran.
2Department of Science, Payame Noor University, PO BOX 19395-3697 Tehran, Iran.
3Department of Applied Mathematics, Mathematical Science Faculty, University of Tabriz, Tabriz, Iran.
چکیده
In this paper, we discuss the new generalized fractional operator. This operator similarly conformable derivative satisfies properties such as the sum, product/quotient, and chain rule. Laplace transform is defined in this case, and some of its properties are stated. In the following, the Sturm-Liouville problems are investigated, and also eigenvalues and eigenfunctions are obtained. 
کلیدواژه‌ها
Fractional Sturm-Liouville؛ Conformable derivative؛ Mittag-Leffler functions؛ Eigenvalues
مراجع
  • [1]         S. Abbasbandy and A. Shirzadi, Homotopy analysis method for multiple solutions of the fractional Sturm-Liouville problems, Numer Algor. 54 (2010), 521-532.
  • [2]         M. A. AL-Gwaiz, Sturm-Liouville theory and its applications, springer - verlage, London, 2008.
  • [3]         Q. M. Al-Mdallal, An efficient method for solving fractional Sturm-Liouville problems, Chaos Soluitions Fractals, 40 (2009), 138-189.
  • [4]         Q. M. AL-Mdallal, T. Abdeljawad, and M. A. Hajji, Theorical and Computational prespectives on eigen- valuse of fourth-order fractional Sturm-Liouville problem, International Journal of Computer Science, DOI: 10.108010027160.2017.1322690.
  • [5]         F. V. Atkinson and A. B. Mingarelli, Asymptotics of the number of zeros and the eigenvalues of general wieghted sturm-liouville problems, J. fur die reine angewandte Math, (Crelle), 375–376, (1987), 380-393.
  • [6]         B.S. Attili and D. Lesnic, An efficient method for computing eigenelements of Sturm-Liouville fourth-order bound- ary value problems, Applied Mathematics and Computation, 182(2) (2006), 1247–1254.
  • [7]         A. M. Cohen, Numerical method for Laplace transform inversion, springer, New York (2007).
  • [8]         M. Dehghan, A. B. Mingarelli, Fractional Sturm-Liouville eigenvalue problems, I, arXiv preprint arXiv:1712.09891, 2017.
  • [9]         M. Dehghan, A. B. Mingarelli, Fractional Sturm-Liouville eigenvalue problems, II, arXiv preprint arXiv:1712.09894, 2017.
  • [10]       F. Jarad and T. Abdeljawad, A modified Laplace transform for certain generalized fractional operators, Res. Nonlinear Anal. 1(2), 88–98 (2018).
  • [11]       E. J. N´apoles Vald´s, and C. Tun¸c, On the Boundedness and Oscillation of Non-conformable Lienard Equation, J. Fract. Calc. Appl., 11(2) (2020), 92-101.
  • [12]       J. He, The variational iteration method for eighth-order initial-boundary value problems, Phys. Scr., 76 (2007), 680-682.
  • [13]       U. N. Katugampola, A new fractional derivative with classical properties, e-print arXiv:1410.6535, (2014).
  • [14]       R. Khalil, M. Al Horani, A. Yousef, and M. Sababhehb, A new definition of fractional derivative, J. Comp. Applied Math., 264 (2014), 65—70.
  • [15]       H. Khan, C. Tun¸c and A. Khan, Green function’s properties and existence theorems for nonlinear singular-delay- fractional differential equations with p-Laplacian, Discrete Contin. Dyn. Syst. Ser. S., 13(9) (2020), 2475–2487.
  • [16]       N. A. Khan, O. A. Razzaq, and M. Ayaz, some properties and application of confomable fractional (CFLT), Journal of Fractional Calculus and Applications. 9(1) (2018), 72–81.
  • [17]       A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and application of fractional differential equations, Elsevier, Amsterdam, 2006.
  • [18]       M. Klimek and O. P. Agrawal, Fractional Sturm-Liouville problem, Computers and Mathematics with Applica- tions, 66(5) (2013), 795 - 812.
  • [19]       Y. Luchko, Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation, Fract. Calc. Appl. Anal, 15(1) (2012), 141–160.
  • [20]       F. Martinez, P. O. Mohammed, and E. J. N´apoles Vald´s, NON-CONFORMABLE FRACTIONAL LAPLACE TRANSFORM, Kragujevac Journal of Mathematics. 46(3) (2022), 341–354.
  • [21]       K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, John Wiley and Sons, New York (1993).
  • [22]       A. B. Mingarelli, On generalized and fractional derivatives and their applications to classical mechanics, Journal of Physics A: Mathematical and Theoretical. .
  • [23]       G. M. Mittag-Leffler, Sur la nouvelle function Eα, C. R. Acad. Sci. Paris, 137 (1903), 554–558.
  • [24]       K. B. Oldham and J. Spanier, The Fractional Calculus, Academic, New York, 1974.
  • [25]       I. Podlubny, Fractional differential equations, Academic, New York, 1999.
  • [26]       P. Ravi, Agarwal, and Y. M. Chow, Iterative methods for a fourth order boundary value problem, DOI: 10.1016/0377-0427(84)90058-X.
  • [27]       M. Rivero, J. Trujillo, and M. Velasco, A fractional approach to the Sturm-Liouville problem, Cent. Eur. J. Phy., 11(10) (2013), 1246-1254.
  • [28]       S. Samko, A. Kilbas, and Q. Marichev, Fractional integrals and derivatives, Berlin: Gorden and Breach 1993.
  • [29]       A. Younus, K. Bukhsh, and C. Tun¸c, Existence of resolvent for conformable fractional Volterra integral equations, Appl. Appl. Math., 15(1) (2020), 372—393.
  • [30]       A. Zettl, Sturm-Liouville Theory, Mathematical Surveys and Monographs, vol. 121, American Mathematical Society, 2005.
آمار
تعداد مشاهده مقاله: 691
تعداد دریافت فایل اصل مقاله: 752


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب