Geodesic
Existence and stability results for Hilfer-Katugampola-type fractional implicit differential equations with nonlocal conditions
Salamooni, Ahmad Y. A. 1 ; Pawar, D. D. 1
1 School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded-431606, India
Journal of nonlinear sciences and its applications, Tome 14 (2021) no. 3, p. 124-138.

Voir la notice de l'article provenant de la source International Scientific Research Publications

This article contains a new discussion for Hilfer-Katugampola-type fractional derivative. We establish an existence and uniqueness results of Hilfer-Katugampola-type fractional derivative for implicit differential equations with the help of Schaefer's fixed point theorem and Banach contraction principle. Also, we use the Gronwall's lemma for singular kernels to prove the Ulam-Hyers-Rassias stability results. Further, the examples are given to illustrate our main results.
DOI : 10.22436/jnsa.014.03.02
Classification : 34A08, 26A33, 34B10, 34A12
Keywords: Hilfer-Katugampola-type fractional derivative, implicit differential equation, Schaefer's fixed point theorem, existence, uniqueness, Ulam stability

Salamooni, Ahmad Y. A.  1 ; Pawar, D. D.  1

1 School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded-431606, India 
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Salamooni, Ahmad Y. A. ; Pawar, D. D. . Existence and stability results for Hilfer-Katugampola-type fractional implicit differential equations with nonlocal conditions. Journal of nonlinear sciences and its applications, Tome 14 (2021) no. 3, p. 124-138. doi : 10.22436/jnsa.014.03.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.014.03.02/

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