arXiv subjects

Sagar T. Sutar

Publications and source records attributed to Sagar T. Sutar.

4 recordsLinked to original sources

arXiv2020

On Nonlinear Hybrid Fractional Differential Equations with Atangana-Baleanu-Caputo Derivative

In this paper, we develop the theory of nonlinear hybrid fractional differential equations involving Atangana--Baleanu--Caputo (ABC) fractional derivative. We construct the equivalent fractional integral equation and establish the existence results through it. Further, we build up the theory of inequalities for ABC--hybrid fractional differential equations and use it to examine the uniqueness, existence of a maximal and minimal solution and the comparison results.

math.DS↗

arXiv2020

Implicit Fractional Differential Equations in Banach Spaces via Picard and Weakly Picard Operator Theory

In this paper, by employing fixed-point methods, we obtain the existence and uniqueness results for the nonlinear implicit fractional differential equations in Banach spaces. Further, we obtain the uniqueness, dependence of the solution on the initial condition as well as on the functions involved on the right-hand side by means of Picard and weakly Picard operator theory and Pompeiu--Hausdorff functional.

math.DS↗

arXiv2020

Analysis of Nonlinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative

In the present paper, we determine the estimations on Atangana-Baleanu-Caputo fractional derivative at extreme points. With the assistance of the estimations obtained, we derive the comparison results. Peano's type existence results established for nonlinear fractional differential equations involving Atangana-Baleanu-Caputo fractional derivative. The acquired comparison results are then utilized to deal with the existence of local, extremal and global solution.

math.AP↗

arXiv2018

On Fractional Volterra integrodifferential equations with fractional integrable impulses

We consider a class of nonlinear fractional Volterra integrodifferential equation with fractional integrable impulses and investigate the existence and uniqueness results in the Bielecki's normed Banach spaces. Further, Bielecki--Ulam type stabilities have been demonstrated on a compact interval. A concrete example is provided to illustrate the outcomes we acquired.

math.DS↗