[1] Abdalla, B., On the oscillation of q-fractional difference equations, Adv. Difference Equ., 2017:254(2017), 11 pp.
[2] Abdalla, B., Oscillation of differential equations in the frame of nonlocal fractional derivatives generated by conformable derivatives, Adv. Difference Equ., 2018:107(2018), 15 pp.
[3] Abdalla, B., Abdeljawad, T., On the oscillation of Hadamard fractional differential equations, Adv. Difference Equ., 2018:409(2018), 13 pp.
[4] Abdalla, B., Abdeljawad, T., On the oscillation of Caputo fractional differential equations with Mittag-Leffler nonsingular kernel, Chaos, Solitons and Fractals, 127(2019), 173–177.
[9] Aslıyüce, S., Güvenilir, A.F., Zafer, A., Oscillation criteria for a certain class of fractional order integro-differential equations, Hacet. J. Math. Stat., 46(2017), 199-207.
[10] Aphithana, A., Ntouyas, S.K., Tariboon, J., Forced oscillation of fractional differential equations via conformable derivatives with damping term, Bound. Value Probl., 2019:47(2019), 16 pp.
[11] Atangana, A., Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system, Chaos, Solitons and Fractals, 102(2017), 396–406.
[12] Atangana, A., Baleanu, D., New fractional derivatives with nonlocal and non-singular kernel:Theory and application to heat transfer model, Therm. Sci., 20(2016), 763–769.
[13] Bolat, Y., On the oscillation of fractional order delay differential equations with constant coefficients, Commun. Nonlinear Sci. Numer. Simul., 19(2014), 3988–3993.
[14] Chen, D.X., Oscillation criteria of fractional differential equations, Adv. Difference Equ., 2012:33(2012), 10 pp.
[15] Chen, D.X., Qu, P.X., Lan, Y.H., Forced oscillation of certain fractional differential equations, Adv. Difference Equ., 2013:125(2013), 10 pp.
[16] Grace, S.R., Agarwal, R.P., Wong, P.J.Y., Zafer, A., On the oscillation of fractional differential equations, Fract. Calc. Appl. Anal., 15(2012),
222–231.
[18] Jarad, F., Abdeljawad, T., Alzabut, J., Generalized fractional derivatives generated by a class of local proportional derivatives, Eur. Phys. J. Special Topics, 226(2017), 3457–3471.
[19] Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative, J. Comput. Appl. Math., 264(2014), 65–70.
[20] Kilbas, A.A., Srivastava, M.H., Trujillo, J.J., Theory and Application of Fractional Differential Equations, North Holland Mathematics Studies, 204, 2006.
[21] Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, 1993.
[22] Singh, J., Kumar, D., Baleanu, D., New aspects of fractional Biswas–Milovic model with Mittag–Leffler law, Math. Model. Nat. Phenom., 14(2019), 23 pp.
[23] Sudsutad, W., Alzabut, J., Tearnbucha, C., Thaiprayoon, C., On the oscillation of differential equations in frame of generalized proportional fractional derivatives, AIMS Math., 5(2020), 856–871.
In this paper, we investigate the oscillation of a class of generalized proportional fractional integro-differential equations with forcing term. We present sufficient conditions to prove some oscillation criteria in both of the Riemann-Liouville and Caputo cases. Besides, we present some numerical examples for applicability of our results.
[1] Abdalla, B., On the oscillation of q-fractional difference equations, Adv. Difference Equ., 2017:254(2017), 11 pp.
[2] Abdalla, B., Oscillation of differential equations in the frame of nonlocal fractional derivatives generated by conformable derivatives, Adv. Difference Equ., 2018:107(2018), 15 pp.
[3] Abdalla, B., Abdeljawad, T., On the oscillation of Hadamard fractional differential equations, Adv. Difference Equ., 2018:409(2018), 13 pp.
[4] Abdalla, B., Abdeljawad, T., On the oscillation of Caputo fractional differential equations with Mittag-Leffler nonsingular kernel, Chaos, Solitons and Fractals, 127(2019), 173–177.
[9] Aslıyüce, S., Güvenilir, A.F., Zafer, A., Oscillation criteria for a certain class of fractional order integro-differential equations, Hacet. J. Math. Stat., 46(2017), 199-207.
[10] Aphithana, A., Ntouyas, S.K., Tariboon, J., Forced oscillation of fractional differential equations via conformable derivatives with damping term, Bound. Value Probl., 2019:47(2019), 16 pp.
[11] Atangana, A., Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system, Chaos, Solitons and Fractals, 102(2017), 396–406.
[12] Atangana, A., Baleanu, D., New fractional derivatives with nonlocal and non-singular kernel:Theory and application to heat transfer model, Therm. Sci., 20(2016), 763–769.
[13] Bolat, Y., On the oscillation of fractional order delay differential equations with constant coefficients, Commun. Nonlinear Sci. Numer. Simul., 19(2014), 3988–3993.
[14] Chen, D.X., Oscillation criteria of fractional differential equations, Adv. Difference Equ., 2012:33(2012), 10 pp.
[15] Chen, D.X., Qu, P.X., Lan, Y.H., Forced oscillation of certain fractional differential equations, Adv. Difference Equ., 2013:125(2013), 10 pp.
[16] Grace, S.R., Agarwal, R.P., Wong, P.J.Y., Zafer, A., On the oscillation of fractional differential equations, Fract. Calc. Appl. Anal., 15(2012),
222–231.
[18] Jarad, F., Abdeljawad, T., Alzabut, J., Generalized fractional derivatives generated by a class of local proportional derivatives, Eur. Phys. J. Special Topics, 226(2017), 3457–3471.
[19] Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative, J. Comput. Appl. Math., 264(2014), 65–70.
[20] Kilbas, A.A., Srivastava, M.H., Trujillo, J.J., Theory and Application of Fractional Differential Equations, North Holland Mathematics Studies, 204, 2006.
[21] Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, 1993.
[22] Singh, J., Kumar, D., Baleanu, D., New aspects of fractional Biswas–Milovic model with Mittag–Leffler law, Math. Model. Nat. Phenom., 14(2019), 23 pp.
[23] Sudsutad, W., Alzabut, J., Tearnbucha, C., Thaiprayoon, C., On the oscillation of differential equations in frame of generalized proportional fractional derivatives, AIMS Math., 5(2020), 856–871.