The solutions of time and space conformable fractional heat equations with conformable Fourier transform

[1] K. Oldham, J. Spanier, The Fractional Calculus, Theory and Applications of Differentiation and Integration of Arbitrary Order, Academic Press, 1974.Search in Google Scholar

[2] K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, 1993.Search in Google Scholar

[3] I. Podlubny, Fractional Differential Equations, Academic Press, 1999.Search in Google Scholar

[4] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, 2006.Search in Google Scholar

[5] N. Nyamoradi, Infinitely Many Solutions for a Class of Fractional Boundary Value Problems with Dirichlet Boundary Conditions, Mediterr. J. Math., 11 (2014), 75-87.10.1007/s00009-013-0307-8Search in Google Scholar

[6] R. Garrappa, M. Popolizio, Exponential Quadrature Rules for Linear Fractional Differential Equations, Mediterr. J. Math., 12 (2015), 219-244.10.1007/s00009-014-0396-zSearch in Google Scholar

[7] Y. Jalilian, R. Jalilian, Existence of Solution for Delay Fractional Differential Equations, Mediterr. J. Math., 10 (2013), 1731-1747.10.1007/s00009-013-0281-1Search in Google Scholar

[8] A. Esen, Y. Ucar, N. Yagmurlu, O. Tasbozan, A Galerkin finite element method to solve fractional diffusion and fractional diffusion-wave equations, Math. Model. Anal., 18 (2) (2013), 260-273.10.3846/13926292.2013.783884Search in Google Scholar

[9] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65-70.10.1016/j.cam.2014.01.002Search in Google Scholar

[10] M. Abu Hammad, R. Khalil, Conformable fractional heat differential equation, Int. J. Pure Appl. Math., 94 (2) (2014), 215-221.10.12732/ijpam.v94i2.8Search in Google Scholar

[11] P. K. Kythe, P. Puri, M. R. Schäferkotter, Partial Differential Equations and Mathematica, CRC Press, 1997.Search in Google Scholar

[12] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015) 57-66.Search in Google Scholar

[13] N. T. Negero, Fourier transform methods for partial differential equations, Internat. J. Partial Differ. Equ. Appl., 2 (3) (2014), 44-57. Search in Google Scholar