SOLUTIONS OF LINEAR FRACTIONAL DIFFERENTIAL EQUATIONS OF ORDER ?−?<??<?

In this study, the linear Caputo fractional differential equation of order ?−1

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  • [1] Debnath, L., (2003), Recent applications of fractional calculus to science and engineering, International Journal of Mathematics and Mathematical Sciences, 54, 3413–3442.
  • [2] Ross, B., (1975), A Brief History and Exposition of the Fundamental Theory of Fractional Calculus. Fractional calculus and its Applications, Lecture notes in Mathematics, Springer: Berlin, Germany, 457, 1–36.
  • [3] Oldham, K.B., Spanier, J., (1974), The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, Academic Press: Newyork.
  • [4] Podlubny, I., (1998), Fractional Differential Equations, Volume 198: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their solutions, Mathematics in Science and Engineering, Academic Press: San Diego.
  • [5] Podlubny, I., (2002), Geometric and physical interpretation of fractional integration and fractional differentiation, Fractional Calculus and Applied Analysis 5, 4, 367–386.
  • [6] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., (2006), Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Elsevier: Amsterdam, The Netherlands.
  • [7] Deithelm, K., (2004), The Analysis of Fractional Differential Equations, Volume 2004 of Lecture Notes in Mathematics, Springer: Berlin, Germany.
  • [8] Gorenflo, R., Kilbas, A.A., Mainardi, F., Rogosin S.V., (2014), Mittag-Leffler Functions, Related Topics and Applications, Springer: Berlin, Germany.
  • [9] Pooseh, S., Rodrigues, H.S., Torres, D.F.M., (2011), Fractional Derivatives in Dengue Epidemics, AIP Conf. Proc., 1389, 739–742.
  • [10] Debnath, L., (2003), Recents Applications of Fractional Calculus to Science and Engineering, Int. J. Math. Appl. Sci, 54, 3413–3442.
  • [11] Singh, J., Kumar, D., Kılıçman, A., (2014), Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations, Abstr. Appl. Anal., 2014, 535793.
  • [12] Koeller, R.C., (1984), Applications of Fractional Calculus to the Theory of Viscoelasticity, J. Appl. Mech., 51, 299–307.
  • [13] Saha, R.S., Bera, R.K., (2000), The random walk’s guide to anomalous diffusion: a fractional dynamics approach, Phys. Rep. 339, 2000, 1-77
  • [14] Waggas, G.A., (2010), Application of Fractional Calculus Operators for a New Class of Univalent Functions with Negative Coefficients Defined by Hohlov Operator, Math. Slovaca, 1, 75–82.
  • [15] Aliev, F.A., Aliev, N.A., Safarova, N.A., Gasimova K.G.,, Velieva N.I., (2018), Solution of Linear Fractional-Derivative Ordinary Differential Equations with Constant Matrix Coefficients, Applied and Computational Mathematics, 17, 3, 317-322
  • [16] Demir, A., Erman, S., Özgür, B., and Korkmaz, E., (2013), Analysis of fractional partial differential equations by Taylor series expansion, Boundary Value Problems, 68