Existence results for $\varphi$-Caputo fractional semilinear evolution equations

Authors

  • Walid Benhadda Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
  • Ali El Mfadel Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco; Superior School of Technology, Sultan Moulay Slimane University, Khenifra, Morocco
  • Abderrazak Kassidi Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
  • M'hamed Elomari Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco

DOI:

https://doi.org/10.3842/umzh.v78i7-8.9432

Keywords:

C0-semigroup, nonlocal condition, φ-Caputo fractional derivative, Measure of noncompactness

Abstract

UDC 517.937, 517.98, 517.23

We study the existence of mild solutions for a new class of nonlocal fractional semilinear integrodifferential evolution equations with a nondensely defined closed linear operator involving the generalized \( \varphi \)-Caputo fractional derivative.  By applying two fixed-point theorems for condensing operators, in combination with the \( C_0 \)-semigroup theory and the concept of noncompactness measure, we derive sufficient conditions for the existence of solutions. An illustrative example is presented to highlight the applicability and robustness of our theoretical findings.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 7-8, 2026.

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Published

24.07.2026

Issue

Vol. 78 No. 7-8 (2026)

Section

Research articles