TY - JOUR AU - Agarwal, R. P. AU - Andrade, B. AU - Cuevas, C. PY - 2010 DA - 2010// TI - Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations JO - Nonlinear Anal. VL - 11 UR - https://doi.org/10.1016/j.nonrwa.2010.01.002 DO - 10.1016/j.nonrwa.2010.01.002 ID - Agarwal2010 ER - TY - JOUR AU - Agarwal, R. AU - Hristova, S. AU - O’Regan, D. PY - 2017 DA - 2017// TI - Mittag-Leffler stability for impulsive Caputo fractional differential equations JO - Differ. Equ. Dyn. Syst. UR - https://doi.org/10.1007/s12591-017-0384-4 DO - 10.1007/s12591-017-0384-4 ID - Agarwal2017 ER - TY - JOUR AU - Nashine, H. K. AU - Arab, R. AU - Agarwal, R. P. AU - Sen, M. PY - 2017 DA - 2017// TI - Positive solutions of fractional integral equations by the technique of measure of noncompactness JO - J. Inequal. Appl. VL - 2017 UR - https://doi.org/10.1186/s13660-017-1497-6 DO - 10.1186/s13660-017-1497-6 ID - Nashine2017 ER - TY - CHAP AU - Gorenflo, R. AU - Mainardi, F. ED - Carpinteri, A. ED - Mainardi, F. PY - 1997 DA - 1997// TI - Fractional calculus, integral and differential equations of fractional order BT - Fractals and Fractional Calculus in Continuum Mechanics PB - Springer CY - Wien UR - https://doi.org/10.1007/978-3-7091-2664-6_5 DO - 10.1007/978-3-7091-2664-6_5 ID - Gorenflo1997 ER - TY - BOOK AU - Kilbas, A. A. AU - Srivastava, H. M. AU - Trujillo, J. J. PY - 2006 DA - 2006// TI - Theory and Applications of Fractional Differential Equations PB - Elsevier CY - Amsterdam UR - https://doi.org/10.1016/S0304-0208(06)80001-0 DO - 10.1016/S0304-0208(06)80001-0 ID - Kilbas2006 ER - TY - JOUR AU - Baleanu, D. AU - Agarwal, P. AU - Parmar, R. K. AU - Alqurashi, M. M. AU - Salahshour, S. PY - 2017 DA - 2017// TI - Extension of the fractional derivative of the Riemann–Liouville JO - J. Nonlinear Sci. Appl. VL - 10 UR - https://doi.org/10.22436/jnsa.010.06.06 DO - 10.22436/jnsa.010.06.06 ID - Baleanu2017 ER - TY - JOUR AU - Kıymaz, I. O. AU - Çetinkaya, A. AU - Agarwal, P. PY - 2016 DA - 2016// TI - An extension of Caputo fractional derivative operator and its applications JO - J. Nonlinear Sci. Appl. VL - 9 UR - https://doi.org/10.22436/jnsa.009.06.14 DO - 10.22436/jnsa.009.06.14 ID - Kıymaz2016 ER - TY - JOUR AU - Agarwal, P. AU - Al-Mdallal, Q. AU - Je Cho, Y. AU - Jain, S. PY - 2018 DA - 2018// TI - Fractional differential equations for the generalized Mittag-Leffler function JO - Adv. Differ. Equ. VL - 2018 UR - https://doi.org/10.1186/s13662-018-1500-7 DO - 10.1186/s13662-018-1500-7 ID - Agarwal2018 ER - TY - JOUR AU - Agarwal, P. AU - El-Sayed, A. A. PY - 2018 DA - 2018// TI - Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation JO - Phys. A, Stat. Mech. Appl. VL - 500 UR - https://doi.org/10.1016/j.physa.2018.02.014 DO - 10.1016/j.physa.2018.02.014 ID - Agarwal2018 ER - TY - JOUR AU - Baltaeva, U. AU - Agarwal, P. PY - 2018 DA - 2018// TI - Boundary-value problems for the third-order loaded equation with noncharacteristic type-change boundaries JO - Math. Methods Appl. Sci. VL - 500 UR - https://doi.org/10.1002/mma.4817 DO - 10.1002/mma.4817 ID - Baltaeva2018 ER - TY - JOUR AU - Agarwal, P. AU - Nieto, J. J. AU - Luo, M. -. J. PY - 2017 DA - 2017// TI - Extended Riemann–Liouville type fractional derivative operator with applications JO - Open Math. VL - 15 UR - https://doi.org/10.1515/math-2017-0137 DO - 10.1515/math-2017-0137 ID - Agarwal2017 ER - TY - JOUR AU - Agarwal, P. AU - Jain, S. AU - Mansour, T. PY - 2017 DA - 2017// TI - Further extended Caputo fractional derivative operator and its applications JO - Russ. J. Math. Phys. VL - 24 UR - https://doi.org/10.1134/S106192081704001X DO - 10.1134/S106192081704001X ID - Agarwal2017 ER - TY - JOUR AU - Jain, S. AU - Agarwal, P. AU - Kilicman, A. PY - 2018 DA - 2018// TI - Pathway fractional integral operator associated with 3m-parametric Mittag-Leffler functions JO - Int. J. Appl. Comput. Math. VL - 4 UR - https://doi.org/10.1007/s40819-018-0549-z DO - 10.1007/s40819-018-0549-z ID - Jain2018 ER - TY - JOUR AU - Agarwal, P. PY - 2017 DA - 2017// TI - Some inequalities involving Hadamard-type k-fractional integral operators JO - Math. Methods Appl. Sci. VL - 40 UR - https://doi.org/10.1002/mma.4270 DO - 10.1002/mma.4270 ID - Agarwal2017 ER - TY - BOOK AU - Ruzhansky, M. V. AU - Je Cho, Y. AU - Agarwal, P. AU - Area, I. PY - 2017 DA - 2017// TI - Advances in Real and Complex Analysis with Applications PB - Springer CY - Singapore UR - https://doi.org/10.1007/978-981-10-4337-6 DO - 10.1007/978-981-10-4337-6 ID - Ruzhansky2017 ER - TY - JOUR AU - Mehrez, K. AU - Agarwal, P. PY - 2019 DA - 2019// TI - New Hermite–Hadamard type integral inequalities for convex functions and their applications JO - J. Comput. Appl. Math. VL - 350 UR - https://doi.org/10.1016/j.cam.2018.10.022 DO - 10.1016/j.cam.2018.10.022 ID - Mehrez2019 ER - TY - JOUR AU - Mainardi, F. PY - 1996 DA - 1996// TI - Fractional relaxation-oscillation and fractional diffusion-wave phenomena JO - Chaos Solitons Fractals VL - 7 UR - https://doi.org/10.1016/0960-0779(95)00125-5 DO - 10.1016/0960-0779(95)00125-5 ID - Mainardi1996 ER - TY - JOUR AU - Mainardi, F. PY - 1996 DA - 1996// TI - The fundamental solutions for the fractional diffusion-wave equation JO - Appl. Math. Lett. VL - 9 UR - https://doi.org/10.1016/0893-9659(96)00089-4 DO - 10.1016/0893-9659(96)00089-4 ID - Mainardi1996 ER - TY - JOUR AU - Mainardi, F. AU - Pagnini, G. PY - 2003 DA - 2003// TI - The Wright functions as solutions of the time-fractional diffusion equation JO - Appl. Math. Comput. VL - 141 ID - Mainardi2003 ER - TY - JOUR AU - Mainardi, F. AU - Pagnini, G. AU - Gorenflo, R. PY - 2007 DA - 2007// TI - Some aspects fractional diffusion equations of single and distributed order JO - Appl. Math. Comput. VL - 187 ID - Mainardi2007 ER - TY - JOUR AU - Mainardi, F. AU - Paradisi, P. PY - 2001 DA - 2001// TI - Fractional diffusive waves JO - J. Comput. Acoust. VL - 9 UR - https://doi.org/10.1142/S0218396X01000826 DO - 10.1142/S0218396X01000826 ID - Mainardi2001 ER - TY - JOUR AU - Agrawal, O. P. PY - 2002 DA - 2002// TI - Solutions for a fractional diffusion-wave equation defined in a bounded domain JO - Nonlinear Dyn. VL - 29 UR - https://doi.org/10.1023/A:1016539022492 DO - 10.1023/A:1016539022492 ID - Agrawal2002 ER - TY - JOUR AU - Camargo, R. F. AU - Capelas de Oliveira, E. AU - Vaz, J. PY - 2009 DA - 2009// TI - On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator JO - J. Math. Phys. VL - 50 UR - https://doi.org/10.1063/1.3269587 DO - 10.1063/1.3269587 ID - Camargo2009 ER - TY - JOUR AU - Hahn, M. AU - Umarov, S. PY - 2011 DA - 2011// TI - Fractional Fokker–Planck–Kolmogorov type equations and their associated stochastic differential equations JO - Fract. Calc. Appl. Anal. VL - 14 UR - https://doi.org/10.2478/s13540-011-0005-9 DO - 10.2478/s13540-011-0005-9 ID - Hahn2011 ER - TY - JOUR AU - Heinsalu, E. AU - Patriarca, M. AU - Goychuk, I. AU - Schmid, G. AU - Hänggi, P. PY - 2006 DA - 2006// TI - Fractional Fokker–Planck dynamics: numerical algorithm and simulations JO - Phys. Rev. E VL - 73 UR - https://doi.org/10.1103/PhysRevE.73.046133 DO - 10.1103/PhysRevE.73.046133 ID - Heinsalu2006 ER - TY - JOUR AU - Kou, S. C. AU - Xie, X. S. PY - 2046 DA - 2046// TI - Generalized Langevin equation with fractional Gaussian noise: subdiffusion within a single protein molecule JO - Phys. Rev. Lett. VL - 93 UR - https://doi.org/10.1103/PhysRevLett.93.180603 DO - 10.1103/PhysRevLett.93.180603 ID - Kou2046 ER - TY - JOUR AU - Lutz, E. PY - 2001 DA - 2001// TI - Fractional Langevin equation JO - Phys. Rev. E VL - 64 UR - https://doi.org/10.1103/PhysRevE.64.051106 DO - 10.1103/PhysRevE.64.051106 ID - Lutz2001 ER - TY - JOUR AU - Mainardi, F. AU - Pironi, P. PY - 1996 DA - 1996// TI - The fractional Langevin equation: Brownian motion revisited JO - Extr. Math. VL - 10 ID - Mainardi1996 ER - TY - JOUR AU - Metzler, R. AU - Barkai, E. AU - Klafter, J. PY - 1999 DA - 1999// TI - Anomalous diffusion and relaxation close to thermal equilibrium: a fractional Fokker–Planck equation approach JO - Phys. Rev. Lett. VL - 82 UR - https://doi.org/10.1103/PhysRevLett.82.3563 DO - 10.1103/PhysRevLett.82.3563 ID - Metzler1999 ER - TY - JOUR AU - Metzler, R. AU - Klafter, J. PY - 2000 DA - 2000// TI - The random walk’s guide to anomalous diffusion: a fractional dynamics approach JO - Phys. Rep. VL - 339 UR - https://doi.org/10.1016/S0370-1573(00)00070-3 DO - 10.1016/S0370-1573(00)00070-3 ID - Metzler2000 ER - TY - CHAP AU - Sandev, T. AU - Tomovski, Z. PY - 2009 DA - 2009// TI - Wave equation for a vibrating string in presence of a fractional friction BT - Proceedings in the Symposium on Fractional Signals and Systems ID - Sandev2009 ER - TY - JOUR AU - Sandev, T. AU - Tomovski, Z. AU - Dubbeldam, J. L. A. PY - 2011 DA - 2011// TI - Generalized Langevin equation with a three parameter Mittag-Leffler noise JO - Physica A VL - 390 UR - https://doi.org/10.1016/j.physa.2011.05.039 DO - 10.1016/j.physa.2011.05.039 ID - Sandev2011 ER - TY - JOUR AU - Sandev, T. AU - Tomovski, Z. PY - 2010 DA - 2010// TI - Asymptotic behavior of a harmonic oscillator driven by a generalized Mittag-Leffler noise JO - Phys. Scr. VL - 82 UR - https://doi.org/10.1088/0031-8949/82/06/065001 DO - 10.1088/0031-8949/82/06/065001 ID - Sandev2010 ER - TY - CHAP AU - Diethelm, K. AU - Weibeer, M. ED - Mehaute, A. L. ED - Machado, J. A. ED - Trigeasson, J. C. ED - Sabatier, J. PY - 2004 DA - 2004// TI - Initial-boundary value problems for time-fractional diffusion-wave equations and their numerical solutions BT - Proceedings of the 1st IFAC Workshop on Fractional Differentiations and Its Applications PB - ENSEIRB CY - Bordeux ID - Diethelm2004 ER - TY - JOUR AU - Luchko, Y. PY - 2011 DA - 2011// TI - Maximum principle and its application for the time-fractional diffusion equations JO - Fract. Calc. Appl. Anal. VL - 14 ID - Luchko2011 ER - TY - JOUR AU - Luchko, Y. PY - 2012 DA - 2012// TI - Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation JO - Fract. Calc. Appl. Anal. VL - 15 UR - https://doi.org/10.2478/s13540-012-0010-7 DO - 10.2478/s13540-012-0010-7 ID - Luchko2012 ER - TY - JOUR AU - Momani, S. PY - 2006 DA - 2006// TI - General solutions for the space- and time-fractional diffusion-wave equation JO - J. Phys. Sci. VL - 10 ID - Momani2006 ER - TY - JOUR AU - Odibat, Z. M. AU - Momani, S. PY - 2006 DA - 2006// TI - Approximate solutions for boundary value problems of time-fractional wave equation JO - Appl. Math. Comput. VL - 181 ID - Odibat2006 ER - TY - JOUR AU - Odibat, Z. M. PY - 2006 DA - 2006// TI - A reliable modification of the rectangular decomposition method JO - Appl. Math. Comput. VL - 183 ID - Odibat2006 ER - TY - JOUR AU - Sandev, T. AU - Metzler, R. AU - Tomovski, Z. PY - 2011 DA - 2011// TI - Fractional diffusion equation with a generalized Riemann–Liouville time fractional derivative JO - J. Phys. A, Math. Theor. VL - 44 UR - https://doi.org/10.1088/1751-8113/44/25/255203 DO - 10.1088/1751-8113/44/25/255203 ID - Sandev2011 ER - TY - JOUR AU - Chen, C. M. AU - Lin, F. AU - Turner, I. AU - Anh, V. PY - 2007 DA - 2007// TI - A Fourier method for the fractional diffusion equation describing sub-diffusion JO - J. Comput. Phys. VL - 227 UR - https://doi.org/10.1016/j.jcp.2007.05.012 DO - 10.1016/j.jcp.2007.05.012 ID - Chen2007 ER - TY - JOUR AU - Sandev, T. AU - Tomovski, Z. PY - 2010 DA - 2010// TI - The general time fractional wave equation for a vibrating string JO - J. Phys. A, Math. Theor. VL - 43 UR - https://doi.org/10.1088/1751-8113/43/5/055204 DO - 10.1088/1751-8113/43/5/055204 ID - Sandev2010 ER - TY - JOUR AU - Tomovski, Z. AU - Sandev, T. PY - 2011 DA - 2011// TI - Effects of a fractional friction with power-law memory kernel on string vibrations JO - Comput. Math. Appl. VL - 62 UR - https://doi.org/10.1016/j.camwa.2011.04.042 DO - 10.1016/j.camwa.2011.04.042 ID - Tomovski2011 ER - TY - JOUR AU - Yuste, S. B. PY - 2006 DA - 2006// TI - Weighted average finite difference methods for fractional diffusion JO - J. Comput. Phys. VL - 216 UR - https://doi.org/10.1016/j.jcp.2005.12.006 DO - 10.1016/j.jcp.2005.12.006 ID - Yuste2006 ER - TY - JOUR AU - Mittag-Leffler, G. M. PY - 1903 DA - 1903// TI - Sur la nouvelle function e(x) JO - C. R. Acad. Sci. Paris VL - 137 ID - Mittag-Leffler1903 ER - TY - JOUR AU - Wiman, A. PY - 1095 DA - 1095// TI - Über den fundamentalsatz in der theorie der funktionen eα(x)$e_{\alpha }(x)$ JO - Acta Math. VL - 29 UR - https://doi.org/10.1007/BF02403202 DO - 10.1007/BF02403202 ID - Wiman1095 ER - TY - JOUR AU - Prabhakar, T. R. PY - 1971 DA - 1971// TI - A singular integral equation with a generalized Mittag-Leffler function in the kernel JO - Yokohama Math. J. VL - 19 ID - Prabhakar1971 ER - TY - BOOK AU - Rainville, E. D. PY - 1960 DA - 1960// TI - Special Functions PB - Macmillan Co. CY - New York ID - Rainville1960 ER - TY - JOUR AU - Srivastava, H. M. AU - Tomovski, Z. PY - 2009 DA - 2009// TI - Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel JO - Appl. Math. Comput. VL - 211 ID - Srivastava2009 ER - TY - JOUR AU - Tomovski, Z. AU - Hilfer, R. AU - Srivastava, H. M. PY - 2010 DA - 2010// TI - Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions JO - Integral Transforms Spec. Funct. VL - 21 UR - https://doi.org/10.1080/10652461003675737 DO - 10.1080/10652461003675737 ID - Tomovski2010 ER - TY - BOOK AU - Caputo, M. PY - 1969 DA - 1969// TI - Elasticita Dissipacione PB - Zanichelli CY - Bologna ID - Caputo1969 ER - TY - BOOK AU - Podlubny, I. PY - 1999 DA - 1999// TI - Fractional Differential Equations PB - Academic Press CY - San Diego ID - Podlubny1999 ER - TY - BOOK AU - Titchmarsh, E. C. PY - 1937 DA - 1937// TI - Introduction to the Theory of Fourier Integrals PB - Chelsea CY - New York ID - Titchmarsh1937 ER -