### On the Initial Value Problem for Fuzzy Nonlinear Fractional Differential Equations

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**Authors:**A. EL MFADEL, S. MELLIANI AND M. ELOMARI

**DOI:**10.46793/KgJMat2105.709K

**Abstract:**

In this paper, we introduce some Simpson’s type integral inequalities via the Katugampola fractional integrals for functions whose ﬁrst derivatives at certain powers are s-convex (in the second sense). The Katugampola fractional integrals are generalizations of the Riemann–Liouville and Hadamard fractional integrals. Hence, our results generalize some results in the literature related to the Riemann–Liouville fractional integrals. Results related to the Hadamard fractional integrals could also be derived from our results.

**Keywords:**

Simpson’s type inequalities, Hölder’s inequality, s-convexity, Katugampola fractional integrals, Riemann–Liouville fractional integrals, Hadamard fractional integrals.

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