NEW CLASS OF CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS AND SOLVABILITY IN DOUBLE SEQUENCE SPACE m2(ϕ)

Kayvanloo H. A., Mehravaran H., Mursaleen M.

Mathematical Foundations of Computing, vol.9, pp.166-176, 2026 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 9
  • Publication Date: 2026
  • Doi Number: 10.3934/mfc.2025014
  • Journal Name: Mathematical Foundations of Computing
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.166-176
  • Keywords: Double sequence space, fractional differential equations, Hausdorff measure of noncompactness, Meir-Keeler condensing operator.
  • Uşak University Affiliated: No

Abstract

First, we define a new class of Caputo fractional differential equations of order 3 < ȷ ≤ 4. Then, we show that m2(ϕ) is a Banach space, and we define a new Hausdorff measure of noncompactness (MNC) in this space. Then, by the new MNC, we discuss the existence of solutions of infinite systems of a new class of fractional differential equations in double sequence space m2(ϕ). Finally, we present an example to show the efficiency of our results