Abstract. In this paper we will consider a nonlinear fractional differential equation with weighted initial and nonlocal conditions and will obtain monotone solution by the sequence of successive approximations starting at a lower solution converges monotonically to the solution of the related Cauchy type weighted nonlocal fractional differential equation under some suitable conditions. MSC2010: 5G10, 47H09, 47H10.
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 < ∞, we consider the fractional differential equationwhere D α and D β i are Riemann Liouville fractional derivatives of order 0 < α, βi ≤ 1.Under some assumptions the nonlocal weighted Cauchy type fractional differential equation and result on its solution will be discussed in nonlinear fractional differential equation.
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