Abstract
In the current manuscript, we study the uniqueness and Ulam-stability of solutions for sequential fractionalpantograph differential equations with nonlocal boundary conditions. The uniqueness of solutions is es-tablished by Banach's fixed point theorem. We also define and study the Ulam-Hyers stability and theUlam-Hyers-Rassias stability of mentioned problem. An example is presented to illustrate the main results.
Highlights
Dierential equations of arbitrary order have recently been studied by many researchers, these equations will be used to describe phenomena of real world problems
We study the uniqueness and Ulam-stability of solutions for sequential fractional pantograph dierential equations with nonlocal boundary conditions
Many interesting and important area concerning of research for dierential equations with fractional calculus are devoted to the existence theory and stability analysis of the solutions, for instance, for instance, see papers [4, 7, 9, 12, 17, 24]
Summary
Dierential equations of arbitrary order have recently been studied by many researchers, these equations will be used to describe phenomena of real world problems. The sequential fractional pantograph dierential equations (1) is Ulam-Hyers stable if there exists a real number λφ > 0 such that for each μ > 0 and for each solution v ∈ W of the inequality. The sequential fractional pantograph dierential equations (1) is Ulam-Hyers-Rassias stable with respect to h ∈ W if there exists a real number λφ > 0 such that for each μ > 0 and for each solution v ∈ W of the inequality. The sequential fractional pantograph dierential equations (1) is generalized Ulam-HyersRassias stable with respect to h ∈ C (J, R+) if there exists a real number λφ,h > 0 such that for each solution v ∈ W of the inequality.
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