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Application of topological degree method in quantitative behavior of fractional differential equations

ur Rahman Ghaus (Department of Mathematics & Statistics, University of Swat, KP Pakistan), dr.ghaus@uswat.edu.pk
Ahmad Saeed (Department of Mathematics, University of Malakand, Lower Dir, KP Pakistan), saeedahmad@uom.edu.pk
Haq Fazal (Department of Mathematics, University of Hazara, KP Pakistan), fazalhaqphd@gmail.com

In the present manuscript we incorporate fractional order Caputo derivative to study a class of non-integer order differential equation. For existence and uniqueness of solution some results from fixed point theory is on our disposal. The method used for exploring these existence results is topological degree method and some auxiliary conditions are developed for stability analysis. For further elaboration an illustrative example is provided in the last part of the research article.

Keywords: Fixed point theorem, Existence and uniqueness, Fractional differential equations