Abstract
In this paper, we discuss the existence and uniqueness of solutions for a boundary value problem of nonlinear Hadamard fractional differential equations and nonlocal non-conserved boundary conditions in terms of Hadamard integral. Our results are new in the present configuration and are based on some classical ideas of fixed point theory. We present several examples for the illustration of main results. A companion problem has also been studied. The paper concludes with some interesting observations.
Highlights
In this paper, we study the following boundary value problem: ⎧ ⎩x( ) =, A (γ ) ηγ x(s) s ds + Bx(e) =c, γ >, < η < e, ( . )
1 Introduction In this paper, we study the following boundary value problem:
The objective of this paper is to investigate a fractional integral boundary value problem involving Hadamard fractional derivative and integral
Summary
Where Dα is the Hadamard fractional derivative of order α, f : [ , e] × R → R is a given continuous function, and A, B, c are real constants. [ ] The Hadamard fractional integral of order q for a function g is defined as (log η)γ where I(·) denotes the Hadamard fractional integral
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