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The aim of this paper is to establish the existence and uniqueness results for implicit differential equations of Hilfer-type fractional order via Schaefer’s fixed point theorem and Banach contraction principle.… Click to show full abstract
The aim of this paper is to establish the existence and uniqueness results for implicit differential equations of Hilfer-type fractional order via Schaefer’s fixed point theorem and Banach contraction principle. Next, we establish the equivalent mixed-type integral for nonlocal condition. Further we prove the Ulam stability results. The Gronwall’s lemma for singular kernels plays an important role to prove our results. We verify our results by providing examples.
Keywords:
implicit differential;
existence stability;
stability results;
differential equations;
results hilfer
Journal Title: Mediterranean Journal of Mathematics
Year Published: 2018
Link to full text (if available)
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Journal Title: Mediterranean Journal of Mathematics
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!