Searcharxiv⌕ Search

arXiv subjects

Ahmad Y. A. Salamooni

Publications and source records attributed to Ahmad Y. A. Salamooni.

6 recordsLinked to original sources
arXiv2020

Existence and Continuation of Solutions of Hilfer-Katugampola-Type Fractional Differential Equations

This article contains a new discussion for the generalized fractional Cauchy-type problem involving Hilfer-Katugampola-type fractional derivative. We study an existence and continuation of its solution. Firstly, we establish a new theorems of local existence. Then, we deduce a continuation theorems for a general fractional differential equations. By applying continuation theorems deduced in this article, we present several global existence results. Moreover, the examples are given to illustrate our main results.

math.AP↗
arXiv2019

Unique positive solution for nonlinear Caputo-type fractional $q$-difference equations with nonlocal and Stieltjes integral boundary conditions

This paper contain a new discussion for the type of generalized nonlinear Caputo fractional $q$-difference equations with $m$-point boundary value problem and Riemann-Stieltjes integral $\tildeα[x]:=\int_{0}^{1}~x(t)dΛ(t).$ By applying the fixed point theorem in cones, we investigate an existence of a unique positive solution depends on $λ>0.$ We present some useful properties related to the Green's function for $m-$point boundary value problem.

math.AP↗
arXiv2019

Katugampola Fractional Calculus With Generalized $k-$Wright Function

In this article, we presented some properties of the Katugampola fractional integrals and derivatives. Also we studied the fractional calculus properties involving Katugampola Fractional integrals and derivatives of generalized $k-$Wright function $_{n}Φ_{m}^{k}(z).$\\[2mm]

math.AP↗
arXiv2018

Existence and Uniqueness of Nonlocal Boundary Conditions for Hilfer-Hadamard-Type Fractional Differential Equations

In this paper, we used some theorems of fixed point for studying the results of existence and uniqueness for Hilfer-Hadamard-Type fractional differential equations, \[_{H}D^{α,β}x(t)+f(t,x(t))=0, \hbox{ on the interval } J:=(1,e]\] with nonlinear boundary value problems \[x(1+ε)=\sum_{i=1}^{n-2}ν_{i}x(ζ_{i}), \quad\quad\quad~_{H}D^{1,1}x(e) = \sum_{i=1}^{n-2} σ_i~_{H} D^{1,1}x(ζ_{i})\]

math.AP↗
arXiv2018

Hilfer-Hadamard-Type Fractional Differential Equation with Cauchy-Type Problem

In this paper, we consider the Cauchy-type problem (1.1) involving Hilfer-Hadamard-type fractional derivative for a nonlinear fractional differential equation. We prove an equivalence between the Cauchy-type problem (1.1) and Volterra integral equation(VIE), existence, and uniqueness. We present a slight generalization for the Gronwall inequality which was used in studying the continuous dependence of a solution for the Cauchy-type problem (1.2).

math.AP↗