Existence Results for Anti-periodic of a Generalized Fractional Derivative Differential Equations

Year 2022, Volume: 5 Issue: 1, 74 - 83, 28.06.2022

Kadda Maazouz , Dvivek Vivek , Elsayed Elsayed

https://doi.org/10.53508/ijiam.1076598

Cited By: 1

Abstract

We study in the present work the existence of solutions to antiperiodic boundary value problem for differential equations involving generalized fractional derivative via fixed point methods.

Keywords

Generalized Fractional Derivative, Antiperiodic Boundary Value Problem, Integral Equation, Fixed Point

Supporting Institution

-

Project Number

-

References

• R.P. Agarwal , B. Ahmad, Existence theory for anti-periodic boundary value problems of fractional differential equations and inclusions
• B. Ahmad, J.J. Nieto, Existence of solutions for impulsive anti-periodic boundary value problems of fractional order
• M. Ashordia, On the solvability of the antiperiodic boundary value problem for systems of linear generalized differential equations
• M. Benchohra, K. Maazouz, Existence and uniqueness results for implicit fractional differential equations with integral boundary conditions, Communications in Applied Analysis,20(2016),355-366.
• A. Cabada, K. Maazouz, Results for Fractional Differential Equations with Integral Boundary Conditions Involving the Hadamard Derivative. In: Area I. et al. (eds) Nonlinear Analysis and Boundary Value Problems. NABVP 2018. Springer Proceedings in Mathematics & Statistics, vol 292. Springer, Cham (2019).
• G. Chai, Anti-periodic boundary value problems of fractional differential equations with the Riemann-Liouville fractional derivative Fractional Differential Equations
• R. Hakl, A. Lomtatidze, and J.???Sremr, On a boundary-value problem of antiperiodic type for first-order nonlinear functional differential equations of nonVolterra type
• U.N. Katugampola, New approach to generalized fractional integral, Appl. Math. Comput. 218(3) (2011), 860-865.
• U.N Katugampola, New approach to generalized fractional derivative, Bull. Math. Anal. Appl. 6 (4) (2014), 1-15.
• D. R. Smart, Fixed Point Theorems, Cambridge University Press, Cambridge 1974.
• D. Vivek, K. Kanagarajan, S. Harikrishnan, Theory and analysis of impulsive type pantograph equations with Katugampola fractioanl derivative, J. Vabration Testing and System Dynamic, 2 (1) 2018, 9-20.
• D. Vivek, E.M. Elsayed, K. Kanagarajan, Theory of fractional implicit differential equations with complex order, Journal of Universal Mathematics, 2 (2) (2019), 154-165.
• X. Li, F. Chen, Xuezhu Li, Generalized anti-periodic boundary value problems of impulsive fractional differential equations
• X. Wang X. Guo G. Tang, Anti-periodic fractional boundary value problems for nonlinear differential equations of fractional order