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In this paper, we study boundary value problem of system of generalized Sturm–Liouville and Langevin Hadamard fractional differential equations. Existence and uniqueness results are proved via Banach contraction principle and Leray–Schauder fixed point theorem. Besides, the Ulam–Hyers and Ulam–Hyers–Rassias stability results are addressed for the proposed problem. An example illustrating the effectiveness of the theoretical results is presented.

We examine a class of nonlinear fractional Mathieu equations with a damping term. The equation is an important equation of mathematical physics as it has many applications in various fields of the physical sciences. By utilizing Schauder’s fixed-point theorem, the existence arises of solutions for the proposed equation with the Hilfer–Katugampola fractional derivative, and an application is additionally examined. Two examples guarantee the obtained results.

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