Geodesic
Theoretical analysis for a system of nonlinear $\phi$-Hilfer fractional Volterra-Fredholm integro-differential equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 2, pp. 216-229.

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We investigate the existence of solutions for a system of nonlinear $\phi$-Hilfer fractional Volterra–Fredholm integro-differential equations with fractional integral conditions, by using the Krasnoselskii's fixed point theorem and Arzela–Ascoli theorem. Moreover, applying an alternative fixed point theorem due to Diaz and Margolis, we prove the Kummer stability of the system on the compact domains. An example is also presented to illustrate our results.
Keywords: $\phi$-Hilfer fractional Volterra-Fredholm integro-differential equation, Kummer's stability, Arzela–Ascoli theorem, Krasnoselskii fixed point theorem. 
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Ahmed A. Hamoud; Nedal M. Mohammed; Rasool Shah. Theoretical analysis for a system of nonlinear $\phi$-Hilfer fractional Volterra-Fredholm integro-differential equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 2, pp. 216-229. http://geodesic.mathdoc.fr/item/JSFU_2023_16_2_a6/

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