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STABILITY ANALYSIS FOR A GENERALIZED PROPORTIONAL FRACTIONAL LANGEVIN EQUATION WITH VARIABLE COEFFICIENT AND MIXED INTEGRO–DIFFERENTIAL BOUNDARY CONDITIONS
Abdellatif Boutiara  1, @  
1 : Laboratory of Mathematics And Applied Sciences, University of Ghardaia, 47000. Algeria  -  Website
Ghardaia-algeria -  Algeria

In this paper, we study the Langevin equation within the generalized proportional fractional derivative. The proposed equation involves a variable coefficient and subjects to mixed integrodifferential boundary conditions. We introduce the generalized proportional fractional derivative and expose some of its features. We mainly investigate the existence, uniqueness and different types of Ulam stability of the solutions via fixed point theorems and inequality techniques. Finally, we provide two examples to support our main results.

Subject : : Oral
Topics : Mathematical analysis
Keywords : Fractional Langevin equation ; Generalized proportional fractional derivative ; Ulam stability ; Existence and Uniqueness ; Fixed point theorem
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