[1] Sun H, Zhang Y, Baleanu D, Chen W and Chen Y 2018 Commun. Nonlinear Sci. Numer. Simul. 64 213-231 [2] Sheng H, Chen Y and Qiu T 2006, Fractional processes and fractional-order signal processing: techniques and applications (Springer Science & Business Media), p. 23 [3] Rahman Z, Alam M and Dover J 2006 Skin Therapy Letter 11 7 [4] Bao C, Pu Y and Zhang Y 2018 Comput. Intell. Neurosci. 2018 7361628 [5] Shah P and Agashe S 2016 Mechatronics 39 29 [6] Lonescu C, Lopes A, Copot D, Tenreiro Machado J and Bates J 2017 Commun. Nonlinear Sci. Numer. Simul. 51 141 [7] Del-Castillo-Negrete D, Carreras B and Lynch V 2005 Phys. Rev. Lett. 94 065003 [8] Tong D, Wang R and Yang H 2005 Phys. Rev. Lett. 48 485-495 [9] Gao C, Zhou J and Liu C 2015 Int. J. Mach. Learn. Cyb. 6 35 [10] Hartley T, Lorenzo C and Killory Qammer H 1995 IEEE Trans. Circ. Sys. I 42 485 [11] Rajagopal K, Duraisamy P and Tadesse G 2021 Int. J. Nonlinear Sci. Num. 2020 0127 [12] Wang M, Wang X and Niu Y 2011 Chin. Phys. B 20 010508 [13] Wu X and Shen S 2009 Int. J. Comput. Math. 86 795360200 [14] Li C and Chen G 2004 Chaos Solitons Fract. 22 549 [15] Xu Z and Liu C 2008 Chin. Phys. B 17 4033 [16] Lu J 2006 Phys. Lett. A 354 305-311 [17] Wu X, Lu H and Shen S 2009 Phys. Lett. A 373 2329 [18] He J and Chen F 2017 Phys. Lett. A 95 73 [19] He S, Sun K and Wang H 2016 Math Method Appl. Sci. 39 2965 [20] Ahmad W and Reyad E 2007 Chaos Solitons Fract. 33 1367 [21] Adolfsson K, Enelund M and Olsson P 2005 Mech. Time-Depend Mater. 9 15 [22] Chen W 2008 Chaos Solitons Fract. 36 1305 [23] Li X, Mou J, Xiong L, Wang Z and Xu J 2021 Opt. Laser Technol. 140 107074 [24] Fataf N, Abdul Rahim M, He S and Banerjee S 2021 Internet of Things 15 100425 [25] Liouville J 1832 Ecole polytechnique 15 71 [26] Riemann B, Dedekind R and Weber H 1847 Versuch einer allgemeinen auffassung der integration und differentiation, Leipzig, Germany, p. 1847 [27] Cristina Caputo M and Torres Delfim F M 2015 Signal Process 107 265 [28] Cristina Caputo M and Torres Delfim F M 2016 Proceedings of the 2016 International Conference on Education, May 2016, Shenyang, P. R. China, p. 553 [29] Podlubny I 1998 Fractional differential equations (Academic Press) p. 62 [30] Khalil R, Horani M, Yousef A and Sababheh M 2014 J. Comput. Appl. Math. 264 65 [31] Miller Kenneth S 1975 The Weyl fractional calculus (Springer, Berlin, Heidelberg) p. 80 [32] Atangana A and Qureshi S 2019 Chaos Solitons Fract. 123 320 [33] Atangana A, Akgul A and Owolabi K M 2020 Alexandria Eng. J. 59 1117 [34] Al-Refai M and Pal K 2019 Prog. Fract. Differ. Appl. 5 157-166 [35] Toufik M and Atangana A2022 Eur. Phys. J. Plus 137 191 [36] Abro K and Atangana A 2021 Arab. J. Sci. Eng. 46 857 [37] Adomian G1984 J. Math. Anal. Appl. 102 420 [38] He J 2008 Topol Methods Nonlinear Anal. 31 205 [39] Arikoglu A and Ozkol I 2007 Chaos, Solitons Fract. 34 1473 [40] He J 2011 Phys. Lett. A 375 3362 [41] Diethelm K and Freed A 1998 Forschung Und Wissenschaftliches Rechnen 57 [42] Sweilam N and Assiri T 2015 Appl. Math. Inf. Sci. 9 943 [43] Charef A, Sun H, Tsao Y and Onaral B1992 IEEE Trans. Autom. Control 37 1465 [44] Liang S, Wu R and Chen L 2015 Electron. J. Differ. Equ 139 1 [45] Shivanian E and Jafarabadi A 2018 Chaos, Solitons Fract. 110 138 [46] Deng W 2009 SIAM J. Numer. Anal. 47 204 [47] Li C, Chen A and Ye J 2011 J. Comput. Phys. 230 3352 [48] Tavazoei M 2020 Eur. Phys. J. Special Topics 229 887 [49] Shrirao N, Pandey A, Chaurasia V, Gupta R, Modi N and Malpani R 2019 Proceedings of the International Conference on Advances in Electronics, Electrical & Computational Intelligence(ICAEEC), April 20, Prayagraj, India pp. 1-9 [50] Tariq M, Shafi R and Munir B 2017 Proceedings of the 2017 International Conference on Robotics and Artificial Intelligence, December 29-31, Shanghai China, pp. 96-100 [51] Ortigueira M and Tenreiro Machado J 2015 J. Comput. Phys. 293 4 [52] Fernandez A and Baleanu D 2021 Math. Methods Appl. Sci 44 9143 [53] Garrappa R 2018 Mathematics 6 16 [54] Sun K, Wang X and Sprott J 2010 Int. J. Bifurcat. Chaos 20 1209 [55] Sun K and Sprott J 2009 Int. J. Bifurcat. Chaos 19 1357 [56] Ding J, Sheng L, Sun K and Yang J 2010 Acta Phys. Sin. 59 8385 (in Chinese) [57] Wang H, Sun K and He S 2015 Int. J. Bifurcat. Chaos 25 1550085 [58] Wang Y, Sun K, He S and Wang H 2014 Eur. Phys. J. Special Topics 223 1591 [59] Zhao C, Li S and Lu T 2015 Int. J. Bifurcat. Chaos 25 1550085 [60] Ahmad W and Sprott J 2003 Chaos, Solitons Fract. 16 339-351 [61] Min F, Shao S, Huang W and Wang E 2015 Chin. Phys. Lett. 32 030503 [62] Jia H, Chen Z and Qi G 2014 IEEE Trans Circuits Syst I Regul Pap 61 845 [63] Lu J and Liu C 2007 Chin. Phys. 16 1586 [64] Takougang Kingni S, Pham V T, Jafari S, Richard Kol G and Woafo P 2016 Circuit, Syst. Signal Process 35 1933 [65] Teng L, Herbert H C Iu, Wang X Y and Wang X K 2014 Nonlinear Dyn. 77 231 [66] Kai D, Neville J F and Alan D F 2004 Numer. Algorithms 36 31 [67] Garrappa R 2010 Int. J. Comput. Math. 87 2281 [68] Kai D and Neville J F 2002 J. Math. Anal. Appl. 265 229 [69] Roberto G 2021 Predictor-corrector pece method for fractional differential equations [70] Bhalekar S and Daftardar-Gejji V 2011 J. Frac. Calc. Appl. 5 1 [71] Kumar M and Daftardar-Gejji V 2019 Appl. Math. Comput. 363 124633 [72] Deng W 2007 J. Comput. Math. 206 174 [73] Mekkaoui T, Atangana A and Igret Araz S 2007 Eng. Comput. 37 2359 [74] Shahbazi Asl M, Javidi M and Ahmad B 2019 J. Appl. Anal. Comput. 9 1527 [75] Ye H and Ding Y 2009 Math. Probl. Eng. 2009 378614 [76] Zhang Z, Zeb A, Francis Egbelowo O and Suat Erturk V 2020 Adv. Differ. Equ. 2020 420 [77] Zhang C and Xiao J 2017 J. Comput. Nonlinear Dyn. 13 021007 [78] Yan B, He S and Wang S 2020 Complexity 2020 1 [79] Shawagfeh N 2002 Appl. Math. Comput. 131 517 [80] Gorenflo R and Mainardi F 1997 Fractals and fractional calculus in continuum mechanics (Springer) pp. 223-276 [81] Wazwaz A 2000 Appl. Math. Comput. 111 33 [82] He S, Sun K and Wang H 2014 Acta Phys. Sin. 63 030502 (in Chinese) [83] Cafagna D and Grassi G 2008 Int. J. Bifurcat. Chaos 18 1845 [84] Cafagna D and Grassi G 2009 Int. J. Bifurcat. Chaos 19 339 [85] Chen H, Lei T, Lu S, Dai W, Qiu L and Zhong L 2020 Complexity 2020 5710765 [86] Caponetto R and Fazzino S 2013 Int. J. Bifurcat. Chaos 23 1350050 [87] Jafari H, Tajadodi H and Baleanu D 2013 Fract. Calc. Appl. Anal. 16 109 [88] Cao F and Lei T 2020 J. Phys.: Conf. Ser. 1550 032043 [89] Zuriqat M and Freihat A 2020 Kyungpook Math. J. 60 753 [90] Liao S2003 Appl. Math. Mech. 24 53 [91] Liao S J 2003 Beyond Perturbation (Chapman and Hall/CRC) p. 179 [92] Yu Y and Li H X 2009 Chaos Soliton Fract. 42 2330 [93] Alomari A K, Noorani M S M, Nazar R and Li C P 2010 Commun. Nonlinear SCI. 15 1864 [94] Alomari A K, Noorani M S M, Nazar R and Li C P 2015 System 15 1864 [95] Veeresha P, Prakasha D G, Abdel-Aty A H, Singh H, Mahmoud E E and Kumar S 2021 J. King Saud University-Sci. 33 101347 [96] Chen C K and Ho S H 1999 Appl. Math. Comput. 106 171 [97] Jassim H K and Vahidi J 2021 Int. J. Nonlinear. Anal. 12 37 [98] Jornet M 2021 Nonlinear Anal. 209 112340 [99] Alomari A K 2011 Comput. Math. Appl. 61 2528 [100] Freihat A and Momani S 2012 Abstr. Appl. Anal. 2012 934219 [101] Momani S, Freihat A and Al-Smadi M 2014 Abstr. Appl. Anal. 2014 276279 [102] Al-Smadi M, Freihat A, Arqub O A and Shawagfeh N 2015 J. Comput. Anal. Appls. 19 713 [103] He S, Sun K and Wang H 2019 Commun. Nonlinear SCI. 73 146 [104] El-Sayed A M A and Salman S M 2013 J. Fract. Calc. Appl 3 251 [105] Agarwal R P, El-Sayed A M A and Salman S M 2013 Adv. Differ. Equ. 1 1 [106] El-Sayed A M A, Elsonbaty A, Elsadany A A and Matouk A E 2016 Int. J. Bifurcat. Chaos 26 1650222 [107] Raheem El Z F and Salman S M 2013 J. Egypt. Math. Soc. 26 407 [108] El-Sayed A M A, Salman S M and Elabd N A 2016 Appl. Math. Sci 10 503 [109] He S, Fataf N A A, Banerjee S and Sun K 2019 Physica A 526 120904 [110] Wang J, Xiao L, Rajagopal K, Akgul A, Cicek S and Aricioglu B 2021 Symmetry 13 340 [111] Li C and Deng W 2007 Appl. Math. Comput. 187 777 [112] He S, Sun K, Mei X, Yan B and Xu S 2017 Eur. Phys. J. Plus 132 36 [113] Ma C, Mou J, Cao, Y, Liu T and Wang J 2020 Phys. Scr. 95 7 [114] Balc E, Öztürk and Kartal S 2019 Chaos Soliton Fract. 123 43 [115] Yan B and He S 2021 Math. Mod. Meth. Appl. S 44 2439 [116] Haghighatnia S, Toossian Shandiz H and Alfi A 2019 Int. J. Industr. Elect. Cont. Optim. 2 177 [117] Chu X, Xu L and Hu H 2020 Chaos Soliton Fract. 140 110268 [118] Kartal S and Gurcan F 2018 Int. J. Ap. Mat. Com.-Pol. 96 1849 [119] Gürcan F, Kaya G and Kartal S 2019 J. Comput. Nonlinear Dynam. 14 111007 [120] Xin B, Peng W and Guerrini L 2019 Front. Phys. 7 84 [121] Wang Y 2018 Eur. Phys. J. Plus 70 481 [122] Gondal M A, Batool S I and Khan M 2014 J. Vib. Control 20 2530 [123] El-Sayed A A and Agarwal P 2019 Math. Methods App. 42 3978 [124] Saqib M, Khan I and Shafie S 2019 Adv. Differ. Equ. 52 [125] Yuttanan B and Razzaghi M 2019 Appl. Math. Model. 70 350 [126] Raja M A Z, Khan J A and Qureshi I M 2010 Asian Conference on Intelligent Information and Database Systems March 24-26, 2010 Berlin, Heidelberg, pp. 231-240 [127] Gonéalez J A and Pino R 2000 Physica A 276 425 [128] Ahmed E and Elgazzar A S 2007 Physica. A 379 607 [129] Atangana A and Noutchie O 2013 Abstr. Appl. Anal. 2013 470 [130] Patnaik S, Hollkamp J P and Semperlotti F 2020 P. Roy. Soc. A-Math. Phy. 476 20190498 [131] Valério D and Costa J S D2011 P. Roy. Soc. A-Math. Phys. 91 470 [132] Wu G, Deng Z, Baleanu D and Zeng D 2019 Chaos 29 083103 [133] Kang Y, Mao S and Zhang Y 2021 Appl. Math. Model. 97 619 [134] Gao Y and Yin D 2021 Appl. Math. Model. 95 435 [135] He S, Banerjee S and Sun K 2018 Chaos Soliton. Fract. 115 14 [136] Abdeljawad T, Banerjee S and Wu G 2020 Optik 218 163698 [137] Wu F, Gao R, Liu J and Li C 2020 Appl. Math. Comput. 380 125278 [138] P-Azucena A D,T-Cuautle E, M-Pacheco J M and la Fraga L G de 2021 Commun. Nonlinear. Sci. Numer. Simul. 72 516 [139] Ma C, B Shiri, Wu G and Baleanu D 2020 Optik 218 164507 [140] Wu G, Luo M, Huang L and Banerjee S 2020 Nonlinear Dyn. 100 3611-3623 [141] Danca M F and Kuznetsov N 2018 Int. J. Bifurcat. Chaos 28 1850067 [142] Xie W, Xu J, Cai L and Lin Z2017 Int. J. Nonlin. Mech. 92 59 [143] Jia H, Chen Z and Xue W 2013 Acta Phys. Sin. 62 140503 (in Chinese) [144] Danca M F 2015 Nonlinear Dyn. 81 227 [145] T-Cuautle E, P-Azucena A D, G-Fernández O and S-Juárez A 2010 Analog/digital implementation of fractional order chaotic circuits and applications (Springer Nature Switzerland) pp. 96-97 [146] Yang N, Wu C, Jia R and Liu C 2016 Math. Probl. Eng. 2016 6835910 [147] Wang Y, Pu Y and Zhou J 2008 Congress on Image and Signal Processing, May 27-30, 1999, Sanya, China, pp. 331-334 [148] Dorčák L, Terpák J, Petráš I and Dorčáková F 2007 Acta. Montan Slovaca 12 231 [149] Cui L, Lu M, Ou Q, Duan H and Luo W 2020 Chaos Soliton. Fract. 138 109894 [150] Alejandro S J, Esteban T C, Luis G F and Rui L 2020 J. Adv. Res. 25 77 [151] Yao J, Wang K, Huang P, Chen L and Tenreiro Machado J A 2020 J. Adv. Res. 25 97-109 [152] Higazy M and Hamed Y S 2022 Alexandria Eng. J. 60 4177 [153] Tavazoei M S and Haeri M 2007 IET Signal Processing 1 171 [154] Liu T, Yan H, Banerjee S and Mou J 2021 Chaos Solitons Fract. 145 110791 [155] Ye X, Wang X 2021 Phys. Scr 95 075212 [156] Han X, Mou J, Xiong L, Ma C, Liu T and Cao Y 2021 Integration 81 43-55 [157] Yang X, He Y, Li C and Liu C 2020 Complexity 2020 6786832 [158] Roshdy M, Sayed W S, Said L A, Madian A H, Radwan A G and Dessouky M 2020 In 2020 16th ICENCO 51-54 [159] Malik S A and Mir AH 2020 Appl. Math. Model. 81 372 [160] Avalos-Ruiz L F, Zuniga-Aguilar C J, Gomez-Aguilar J F, Escobar-Jimenez G F and Romero-Ugalde H M 2018 Chaos, Solitons Fract. 115 177 [161] El-Maksoud A J A, El-Kader A A A, Hassan B G, Rihan N G, Tolba M F, Said L A, Radwan A G and Abu-Elyazeed M F 2019 Microelectron. J. 90 323 [162] Liu C, Wang D, Li C, Su K, Li D, Yu D, Wang L, Si L and Jin J 2020 In AOPC 2020: Optical Information and Network 11569 1156908 [163] Petras I, Chen Y and Coopmans C 2009 2009 IEEE Conference on Emerging Technologies & Factory Automation September 22-25, 2009, Palma de Mallorca, Spain, p. 1-8 [164] Coopmans C, Petra's I and Chen Y 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference September 1, San Diego, CA, p. 1127-1136 [165] Wang F Z, Shi L, Wu H, Helian N and Chua L O 2017 Appl. Phys. Lett. 111 243502 [166] Fouda M E and Radwan A G 2013 J. Frac. Calc. Appl. 4 1 [167] Rashad S H, Hamed E M, Fouda M E, AbdelAty A M, Said L A and Radwan A G 2017 2017 6th International Conference on Modern Circuits and Systems Technologies (MOCAST) May 4-6, Thessaloniki, Greece, pp. 1-4 [168] Sanchez-Lopez C, Carbajal-Gomez V H, Carrasco-Aguilar M A and Carro-Perez I 2018 Complexity 2018 2806976 [169] Abro K A and Atangana A 2020 Math. Method Appl. Sc. 43 6378 [170] Akgul A, Rajagopal K, DurduDurdu A, Pala M A and Yldz M Z 2021 Chaos, Solitons Fract. 152 11306 [171] He S, Sun K, Peng Y and Wang L 2020 AIP Adv. 10 015332 [172] Peng Y, Sun K and He S 2020 Chaos, Solitons Fract. 137 109873 [173] Petras I 2010 IEEE T. Circuit-II 57 975 [174] Cafagna D and Grassi G 2012 Nonlinear Dyn. 70 1185 [175] Ruan J, Sun K, Mou J, He S and Zhang L 2018 Eur. Phys. J. Plus 133 3 [176] Hu W, Ding D, Zhang Y, Wang N and Liang D 2017 Optik 130 189 [177] Rajagopal K, Karthikeyan A and Srinivasan A 2018 Nonlinear Dyn. 91 1491 [178] Huang X, Jia J, Li Y and Wang Z 2016 Neurocomputing 218 296 [179] Rajagopal K, Li C, Nazarimehr F, Karthikeyan A, Duraisamy P and Jafari S 2019 Radioengineering 28 165 [180] Ma J and Tang J 2017 Nonlinear Dyn. 89 1569 [181] Yan B, He S and Wang S 2020 Math. Probl. En.2020 12 [182] He S 2020 Front. Appl. Math. Stat. 6 24 [183] Aihara K, Takabe T and Toyoda M 1990 Phys. Lett. A 144 333-340 [184] Chen L and Aihara K 1995 Neural networks 8 915 [185] Lin H, Wang C, Yao W and Tan Y 2020 Commun. Nonlinear Sci. 90 105390 [186] Wang Y, Jahanshahi H, Bekiros S, Bezzina F, Chu Y and Aly A A 2021 Chaos, Solitons Fract. 146 110881 [187] Mahmoud E E, Jahanzaib L S and Trikha P 2021Adv. Differ. Equ 2021 126 [188] Fan Y, Huang X, Wang Z and Li Y 2018Nonlinear Dyn. 93 611 [189] Rajchakit G, Kaewmesri P, Chanthorn P, et al. 2020 Mathematics 8 801 [190] Han Z, Li S and Liu H 2020 J. Adv. Res. 25 87 [191] Zhang X, Zhang X, Li D and Yang D 2019 Int. J. Control Autom. Syst. 17 1209 [192] Sun Y and Liu Y 2020 Int. J. Innov. Comput, Inf. Control. 16 649 [193] Vázquez-Guerrero P, Gémez-Aguilar J F, Santamaria F and Escobar-Jiménez R F 2020 Physica A 539 122896 [194] Wen X, Wu Z and Lu J 2008 IEEE Trans. Circ. Sys. II: Express Briefs 55 1178 [195] Raja M A Z, Manzar M A and Samar R 2015 Appl. Math. Model. 39 3075-3093 [196] Pan I and Das S 2012 Intelligent fractional order systems and control: an introduction (Berlin, New York: Springer) pp. 63-84 |