Investigation of a Class of Implicit Anti-Periodic Boundary Value Problems

https://doi.org/10.48185/jmam.v2i1.169

Authors

Keywords:

Anti-periodic boundary value problem, Fixed point theorem, Stability results

Abstract

This research is devoted to studying a class of implicit fractional order differential equations ($\mathrm{FODEs}$) under anti-periodic boundary conditions ($\mathrm{APBCs}$). With the help of classical fixed point theory due to $\mathrm{Schauder}$ and $\mathrm{Banach}$, we derive some adequate results about the existence of at least one solution. Moreover, this manuscript discusses the concept of stability results including Ulam-Hyers (HU) stability, generalized Hyers-Ulam (GHU) stability, Hyers-Ulam Rassias (HUR) stability, and generalized Hyers-Ulam- Rassias (GHUR)stability. Finally, we give three examples to illustrate our results.

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References

Toledo-Hernandez, Rasiel, Vicente Rico-Ramirez, Gustavo A. Iglesias-Silva, and Urmila M. Diwekar, A fractional calculus approach to the dynamic optimization of biological reactive systems.

Part I: Fractional models for biological reactions, Chemecal Engineering Science, 117 (2014) 217-228.

H.A.A. El-Saka, The fractional-order SIS epidemic model with variable population size, J.Egyptian.

Math. Soci. 22 (2014) 50-54.

A.A. Kilbas, H. Srivastava and J. Trujillo, Theory and application of fractional di erential equations, North Holland Mathematics Studies, vol. 204, Elseveir, Amsterdam, 2006.

R. Hilfer, Applications of Fractional Calculus in Physics, World Scienti c, Singapor, 2000.

Published

2021-03-29

How to Cite

Hashtamand, L. (2021). Investigation of a Class of Implicit Anti-Periodic Boundary Value Problems. Journal of Mathematical Analysis and Modeling, 2(1), 47–61. https://doi.org/10.48185/jmam.v2i1.169