On Ulam's type stability criteria for fractional integral equations including Hadamard type singular kernel

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Başcı Y., Öğrekçi S., Mısır A.

TURKISH JOURNAL OF MATHEMATICS, vol.44, no.4, pp.1498-1509, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-1910-70
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1498-1509
  • Keywords: Hyers-Ulam stability, Hyers-Ulam-Rassias stability, fractional integral equation, fixed point theory, Hadamard type singular kernel, DIFFERENTIAL-EQUATIONS, FIXED-POINT, EXISTENCE, BOUNDEDNESS, THEOREMS
  • Gazi University Affiliated: Yes

Abstract

In this paper, we deal with the Hyers-Ulam-Rassias (HUR) and Hyers-Ulam (HU) stability of Hadamard type fractional integral equations on compact intervals. The stability conditions are developed using a new generalized metric (GM) definition and the fixed point technique by motivating Wang and Lin Ulam's type stability of Hadamard type fractional integral equations. Filomat 2014; 28(7): 1323-1331. Moreover, our approach is efficient and ease in use than to the previously studied approaches. Finally, we give two examples to explain our main results.