IJPAM: Volume 108, No. 1 (2016)

SOLUTION TO WEIGHTED NON-LOCAL
FRACTIONAL DIFFERENTIAL EQUATION

Mohammed Mazhar-Ul-Haque$^1$, Tarachand L. Holambe$^2$, Govind P. Kamble$^3$
$^1$Dr. B.A.M. University
Aurangabad, Maharashtra, INDIA
$^2$Department of Mathematics
Kai Shankarrao Gutte ACS College
Dharmapuri, Beed, Maharashtra, INDIA
$^3$Department of Mathematics
P.E.S. College of Engineering
Nagsenvana, Aurangabad, (M.S.) INDIA


Abstract. In this paper we prove the nature and existence of the solutions for a weighted nonlinear fractional differential equation with nonlocal condition. Given a bounded interval $J=(0,T]$ of the real line $\,\R$ for some $T>0$ and $T<\infty$, we consider the fractional differential equation \begin{equation*} \begin{aligned} A_{0}v(t)+\sum_{i=1}^{n}A_{i}D^{\beta_{i}}(v(t... ...{1-\alpha}v(t)u(t)=&\sum_{j=1}^{m}a_{j}u(\tau_{j}), \end{aligned}\end{equation*} where $D^{\alpha}$ and $D^{\beta_{i}}$ are Riemann Liouville fractional derivatives of order $0<\alpha,\beta_{i}\leq1$.

Under some assumptions the nonlocal weighted Cauchy type fractional differential equation and result on its solution will be discussed in nonlinear fractional differential equation.

Received: March 11, 2016

AMS Subject Classification: 26A33, 34K37, 34A08, 45E10, 47H10

Key Words and Phrases: weighted nonlocal problem, nonlinear fractional differential equation, Reimann Liouville integral and derivative, fractional differential equation, fractional integral equation

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DOI: 10.12732/ijpam.v108i1.9 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 1
Pages: 79 - 91


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