arXiv subjects
Publications and source records attributed to Deepak B. Pachpatte.
In this paper, we investigate existence and uniqueness of solutions for Darboux type problem for fuzzy fractional order differential equation. We used Caputo-Katogampola fuzzy fractional derivative for proving our results. Schauder's fixed point theorem is used in proving our results. some applications are also provided to give the usefulness of our results.
In present paper, Hartman-Wintner-type inequality is established for a nonlocal fractional boundary value problem involving k-Prabhakar fractional derivative.
In this paper, we investigate the existence and uniqueness of solution of nonlinear $ψ$-Caputo fractional differential equation with the help of Banach fixed point theorem. Moreover, by using $ψ$-Gronwall inequality, we studied some qualitative properties of solutions such as estimate and stability.
In this paper, we obtain Lyapunov type inequality for discrete fractional boundary value problem.
In this paper, we establish Iyengar type inequalities utilizing $ψ$-Caputo fractional derivatives that is, fractional derivative of a function with respect to another function, which is generalization of some known fractional derivatives such as Riemann-Liouville, Hadamard, Erdélyi-Kober. The inequalities in this article are with respect to $L_{p}$ norms, $1\leq p \leq \infty.$ The tools used in the analysis are based on Taylor's formulae for $ψ$-Caputo fractional derivatives.
In this paper, we studied the sufficient conditions for the existence of positive solutions to the boundary value problems of Caputo fractional difference equations depending on parameters with non local boundary conditions. We construct and analyse the Green's function to the corresponding boundary value problem and then established the existence results using Krasnosel'skii fixed point theorem.
In this paper, we obtained the sufficient conditions for the existence of solutions to the discrete boundary value problems of fractional difference equation depending on parameters. We use Krasnoselskii fixed point theorem to establish the existence results.
In this paper we study some properties of $ψ$-Hilfer fractional integrodifferential equations. We obtain the existence and uniqueness and other properties such as continuous dependence of solution. The tools used for obtaining our result is Banach fixed point theorem. Certain inequalities are also used obtain the estimates on the solution of the equation.
The main objective of this paper is to obtain generalization of some Gruss-type inequalities in case of functional bounds by using a generalized Katugampola fractional integral.
In this paper we obtain a generalization of some integral inequalities related to Chebyshev`s functional by using a generalized Katugampola fractional integral.
In this paper we obtain generalized Gronwall type inequality using Caputo Fractional delta operator. Also we have obtained the existence of solution of Cauchy's Type problem on fractional dynamic equations using dynamic delta operator. Applying the obtained inequality we study the properties of solution on fractional dynamic equations.
The aim of the present paper is to obtain some new fractional integral inequalities for convex functions. Saigo fractional integral operator is used to establish the results.
The purpose of this paper is to study the Hermite-Hadamard type inequality for r-preinvex and (α, m)-preinvex function which is based on Sugeno integral.
In this paper we prove a Hadamard type fuzzy inequality for (s,m)-convex function in second sense and some exam- ples are given.
The main objective of this paper is to obtain some Gruss Like Inequalities using Pompeiu's mean value theorem on Conformable Fractional Calculus.
In this paper, we consider a nonlocal fractional boundary value problem with Prabhakar derivative and obtained a Hartman-Wintner type inequality for it.
The main objective of this paper is to study some Ostrowski and Cebysev type inequalities in three variables on Time Scales
The main objective of this paper is to study some Ostrowski and Trapezoid type inequalities for double integrals on Time Scales. Some other interesting inequalities are also given.