Existence of solutions for a class of nonlinear fractional difference equations of the Riemann–Liouville type

Suwan, I., Owies, S., Abdeljawad, T.: Monotonicity results for h-discrete fractional operators and application. Adv. Differ. Equ. 2018, 207 (2018)

Mohammed, P.O., Hamasalh, F.K., Abdeljawad, T.: Difference monotonicity analysis on discrete fractional operators with discrete generalized Mittag-Leffler kernels. Adv. Differ. Equ. 2021, 213 (2021)

Mohammed, P.O., Abdeljawad, T., Hamasalh, F.K.: On Riemann–Liouville and Caputo fractional forward difference monotonicity analysis. Mathematics 9, 1303 (2021)

Atici, F.M., Nguyen, N., Dadashova, K., Pedersen, S.E., Koch, G.: Pharmacokinetics and pharmacodynamics models of tumor growth and anticancer effects in discrete time. Comput. Math. Biophys. 8, 114–125 (2020)

Xu, J., Goodrich, C.S., Cui, Y.: Positive solutions for a system of first-order discrete fractional boundary value problems with semipositone nonlinearities. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 113, 1343–1358 (2021)

Atici, F., Eloe, P.: A transform method in discrete fractional calculus. Int. J. Differ. Equ. 2, 165–176 (2007)

Sahin, R., Yagci, O.: Fractional calculus of the extended hypergeometric function. Appl. Math. Nonlinear Sci. 5, 369–384 (2020)

Abdeljawad, T.: On delta and nabla Caputo fractional differences and dual identities. Discrete Dyn. Nat. Soc. 2013, Article ID 406910 (2013)

Abdeljawad, T.: Different type kernel h-fractional differences and their fractional h-sums. Chaos Solitons Fractals 116, 146–156 (2018)

Abdeljawad, T., Atici, F.: On the definitions of nabla fractional operators. Abstr. Appl. Anal. 2012, Article ID 406757 (2012)

Sahin, R., Yagci, O.: Fractional calculus involving $(p,q)$-Mathieu type series. Appl. Math. Nonlinear Sci. 5, 15–34 (2020)

Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematical Studies, vol. 204. Elsevier, Amsterdam (2006)

Srivastava, H.M.: Fractional-order derivatives and integrals: introductory overview and recent developments. Kyungpook Math. J. 60, 73–116 (2020)

Srivastava, H.M.: An introductory overview of fractional-calculus operators based upon the Fox–Wright and related higher transcendental functions. J. Adv. Eng. Comput. 5, 135–166 (2021)

Srivastava, H.M.: Some parametric and argument variations of the operators of fractional calculus and related special functions and integral transformations. J. Nonlinear Convex Anal. 22, 1501–1520 (2021)

Goodrich, C.S., Peterson, A.C.: Discrete Fractional Calculus. Springer, Berlin (2015)

Goodrich, C.S.: Discrete Kirchhoff equations with sign-changing coefficients. J. Differ. Equ. Appl. 27, 664–685 (2021)

Atici, F.M., Eloe, P.: Initial value problems in discrete fractional calculus. Proc. Am. Math. Soc. 137, 981–989 (2009)

Meganathan, M., Abdeljawad, T., Motawi Khashan, M., et al.: Analytic and numerical solutions of discrete Bagley–Torvik equation. Adv. Differ. Equ. 2021, 222 (2021)

Mohammed, P.O., Abdeljawad, T.: Discrete generalized fractional operators defined using h-discrete Mittag-Leffler kernels and applications to AB fractional difference systems. Math. Methods Appl. Sci., 1–26 (2020). https://doi.org/10.1002/mma.7083

Khan, A., et al.: Stability analysis of fractional nabla difference COVID-19 model. Results Phys. 22, 103888 (2021)

Atici, F.M., Wu, F.: Existence of solutions for nonlinear fractional difference equations with initial conditions. Dyn. Syst. Appl. 23, 265–276 (2014)

El-Borhamy, M., Mosalam, N.: On the existence of periodic solution and the transition to chaos of Rayleigh–Duffing equation with application of gyro dynamic. Appl. Math. Nonlinear Sci. 5, 93–108 (2020)

Goodrich, C.S.: Existence of a positive solution to a system of discrete fractional boundary value problems. Appl. Math. Comput. 217, 4740–4753 (2011)

Saouli, M.A.: Existence of solution for mean-field reflected discontinuous backward doubly stochastic differential equation. Appl. Math. Nonlinear Sci. 5, 205–216 (2020)

Jonnalagadda, J.: Existence results for solutions of nabla fractional boundary value problems with general boundary conditions. Adv. Theory Nonlinear Anal. Appl. 4, 29–42 (2020)

Lu, Q., Zhu, Y., Lu, Z.: Uncertain fractional forward difference equations for Riemann–Liouville type. Adv. Differ. Equ. 2019, 147 (2019)

Mohammed, P.O.: A generalized uncertain fractional forward difference equations of Riemann–Liouville type. J. Math. Res. 11, 43–50 (2019)

Lu, Q., Zhu, Y.: Comparison theorems and distributions of solutions to uncertain fractional difference equations. J. Comput. Appl. Math. 376, 112884 (2020)

Srivastava, H.M., Mohammed, P.O.: A correlation between solutions of uncertain fractional forward difference equations and their paths. Front. Phys. 8, 280 (2020)

Srivastava, H.M., Mohammed, P.O., Ryoo, C.S., Hamed, Y.S.: Existence and uniqueness of a class of uncertain Liouville–Caputo fractional difference equations. J. King Saud Univ., Sci. 33, 101497 (2021)

Chen, F., Liu, Z.: Asymptotic stability results for nonlinear fractional difference equations. J. Appl. Math. 2012, Article ID 879657 (2012)

Chen, F., Luo, X., Zhou, Y.: Existence results for nonlinear fractional difference equation. Adv. Differ. Equ. 2011, Article ID 713201 (2011)

He, J.W., Zhang, L., Zhou, Y., Ahmad, B.: Existence of solutions for fractional difference equations via topological degree methods. Adv. Differ. Equ. 2018, 153 (2018)

Cheng, S.S., Patula, W.T.: An existence theorem for a nonlinear difference equation. Nonlinear Anal., Theory Methods Appl. 20, 193–203 (1993)

Burton, T.A., Furumochi, T.: Krasnoselskii’s fixed point theorem and stability. Nonlinear Anal., Theory Methods Appl. 49, 445–454 (2002)