Fractional order differential equation with nonlocal integral condition | ||||
| Journal of Fractional Calculus and Applications | ||||
| Volume 15, Issue 1, January 2024, Page 1-10 PDF (306.47 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/jfca.2024.275808.1078 | ||||
 View on SCiNiTO | ||||
| Author | ||||
Antisar Alhamali 
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| Alexandria University | ||||
| Abstract | ||||
| This research paper focuses on investigating the solvability of the Riemann-Liouville di erential equation with nonlocal integral condition, study the existence of solutions in the class of continuous functions, we use the technique of the Schauder xed point Theorem. We drive sucient conditions for a uniqueness and the continuous depen- dence on some functions. Additionally, we delve into the study of the Hyers{Ulam stability. Finally, we given an examples are provided to illustrate our results.The de nition of the fractional derivative of the Riemann-Liouville type played an important role in the development of the theory of fractional derivatives and integrals and for its applications in pure mathematics. However, the demands of modern technology require a certain revision of the well-established pure mathematical approach. Applied problems require de nitions of fractional derivatives allowing the utilization of physically interpretable initial conditions. where RD is the refers to the fractional derivative of Riemann{Liouville of order 2 (0; 1). Our aim here is study the existence of solutions x 2 C(I). Moreover, the continuous dependence of the unique solution on the x0 and on the functions f, g and will be proved. The Hyers { Ulam stability of the problem will be given. | ||||
| Keywords | ||||
| Riemann-Liouville; existence of solution; Hyers{Ulam stability; continuous dependence; fractional order | ||||
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