Abstract
We proved the existence of P-integrable solution in -space, where for the fractional differential equation which has the form: with boundary condition where is the Caputo fractional derivative, and c are positive constants with . The contraction mapping principle has been used to establish our main result.
Highlights
Fractional differential equations have gained importance and popularity during the past three decades or so, due to mainly its demonstrated applications in numerous seemingly diverse fields of science and engineering
Fractional derivatives provide an excellent instrument for the description of memory and hereditary properties of various materials and processes
This is the main advantage of fractional derivatives in Joseph Gh
Summary
Fractional differential equations have gained importance and popularity during the past three decades or so, due to mainly its demonstrated applications in numerous seemingly diverse fields of science and engineering. Fractional derivatives provide an excellent instrument for the description of memory and hereditary properties of various materials and processes. Where a,ci R,i = 1,2,..,n, cn = 0 , f(t,y) is Lebsegue integrable function which satisfies the global Lipschitz condition. Hadid [5] studied local and global existence theorems of the nonlinear differential equation. Momani [8] studied local and global uniqueness theorems of the fractional differential equation (1.3) with the condition (1.4), by using Biharie’s and Gronwell’s inequalities. Benchohra et al [4] studied the existence of solutions for boundary value problems , for fractional differential equation(1.3), for each t J = [0,T ], 0 1 and satisfying the boundary condition y (0) + y (T ) = c. Provided that this integral (lebsegue) exists, where is gamma function. For a function f defined on the interval [a,b], the th derivative of f is defined by
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