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Naseer Ahmad Asif

Publications and source records attributed to Naseer Ahmad Asif.

5 recordsLinked to original sources
arXiv2021

Positive Solution for a Hadamard Fractional Singular Boundary Value Problem of Order $μ\in(2,\,3)$

In this article, we establish the existence of positive solution for the following Hadamard fractional singular boundary value problem \begin{align*} {}^{H}D_{a^{+}}^{\,μ}x(t)+f(t,x(t))&=0,\hspace{0.4cm}t\in(a,\,b),\hspace{0.4cm}0<a<b<\infty,\hspace{0.4cm}2<μ<3,\\ x(a)=a\,x'(a)=x(b)&=0, \end{align*} where $f:(a,\,b)\times(0,\infty)\rightarrow(0,\infty)$ is continuous and singular at $t=a$, $t=b$ and $x=0$. Further, ${}^{H}D_{a^{+}}^{\,μ}$ is Hadamard fractional derivative of order $μ$.

math.CA↗
arXiv2019

Symmetric positive solutions for a fractional singular integro-differential boundary value problem in presence of Caputo-Fabrizio fractional derivative

We introduce the notion of Caputo-Fabrizio left and right derivatives. We present sufficient conditions for the existence of symmetric positive solutions for the following Caputo-Fabrizio fractional singular integro-differential boundary value problem \begin{align*} (2-μ)\,{}^{CF}D_{0}^{\,μ}x(t)+f(t,x(t))&=\left(\frac{μ-1}{2-μ}\right)^{2} \begin{cases} \int_{t}^{0}e^{-\frac{μ-1}{2-μ}(τ-t)}\,x(τ)dτ,\hspace{0.4cm}&t\in(-1,0],\\ \int_{0}^{t}e^{-\frac{μ-1}{2-μ}(t-τ)}\,x(τ)dτ,\hspace{0.4cm}&t\in[0,1), \end{cases}\\ x(\pm1)=x'(0^{\pm})&=0,\hspace{5.55cm}μ\in(1,2), \end{align*} where the nonlinearity $f:(-1,\,1)\times(0,\infty)\rightarrow\mathbb{R}$ is continuous and singular at $t=-1$, $t=1$ and $x=0$.

math.CA↗
arXiv2019

Existence of Symmetric Positive Solutions for a Caputo Fractional Singular Boundary Value Problem

In this article, we establish the symmetric positive existence for the following Caputo fractional boundary value problem \begin{align*} {}^{C}D_{0}^{\,μ}x(t)+f(t,x(t))&=0,\hspace{1cm}t\in(-1,\,1),\hspace{1cm}1<μ\leq2,\\ x(\pm1)=x'(0^{\pm})&=0, \end{align*} where ${}^{C}D_{0}^{\,μ}x(t)={}^{C}D_{0^{+}}^{\,μ}x(t)$ for $t\geq0$, ${}^{C}D_{0}^{\,μ}x(t)={}^{C}D_{0^{-}}^{\,μ}x(t)$ for $t\leq0$. Moreover, $f:(-1,\,1)\times(0,\infty)\rightarrow\mathbb{R}$ is continuous and singular at $t=-1$, $t=1$ and $x=0$. Here, ${}^{C}D_{0^{+}}^{\,μ}$ and ${}^{C}D_{0^{-}}^{\,μ}$, respectively, are Caputo fractional left and right derivatives of order $μ$.

math.CA↗
arXiv2019

Existence and Multiplicity Results for Systems of Singular Boundary Value Problems

Singular boundary value problems (SBVPs) arise in various fields of Mathematics, Engineering and Physics such as boundary layer theory, gas dynamics, nuclear physics, nonlinear optics, etc. The present monograph is devoted to systems of SBVPs for ordinary differential equations (ODEs). It presents existence theory for a variety of problems having unbounded nonlinearities in regions where their solutions are searched for. The main focus is to establish the existence of positive solutions. The results are based on regularization and sequential procedure. First chapter of this monograph describe the motivation for the study of SBVPs. It also include some available results from functional analysis and fixed point theory. The following chapters contain results from author's PhD thesis, National University of Sciences and Technology, Islamabad, Pakistan. These results provide the existence of positive solutions for a variety of systems of SBVPs having singularity with respect to independent and/or dependent variables as well as with respect to the first derivatives of dependent variables.

math.CA↗