TDCS is a rapidly expanding technique, used to treat cognitive difficulties associated with many pathologies (Parkinson's disease, rehabilitation after head trauma, etc.), but which remains of the field of research.

Its use remains very experimental, and concerns the exploration of cognitions, in healthy and diseased subjects. There are not many studies on the elderly subject with Alzheimer's disease, nor do they document the medium- and long-term effect (more than one month), nor the effect on geriatric parameters such as Fragility indices and the risk of falls, especially at home. These characteristics are decisive because they define the level of autonomy.

The investigators therefore wish to study the effect of a 2-week treatment with tDCS (tDCS active) versus placebo (2-week tDCS group) for a three-month period.

Alzheimer's disease and related syndromes have become a major public health priority issue in France. Pharmacological treatments are ineffective and symptomatic, and only delay the progression of the disease.

The management of Alzheimer's disease involves the development of multi-domain prevention programs, including physical activity and neurostimulation by cognitive stimulation. They aim to delay the appearance of fragility defined according to Fried by difficulties in walking, weight loss, fatigue, lack of wrist strength and sedentary lifestyle.

Transcranial direct current stimulation (tDCS) is a stimulation technique using a low intensity DC electric current that acts by modulating neuronal excitability at the cerebral level.

According to recent data, by its action on the cerebral cortex, this simple and non-invasive stimulation technique could prevent the effects of pathological aging, and reduce the cognitive difficulties of the elderly concerning episodic memory, attention and executive functions. These difficulties are also factors related to the risk of the elderly falling (defined by the slowness of walking speed, reduced monopodal support time and the existence of a falling antecedent).

TDCS is a rapidly expanding technique, used to treat cognitive difficulties associated with many pathologies (Parkinson's disease, rehabilitation after head trauma, etc.), but which remains of the field of research.

Its use remains very experimental, and concerns the exploration of cognitions, in healthy and diseased subjects. There are not many studies on the elderly subject with Alzheimer's disease, nor do they document the medium- and long-term effect (more than one month), nor the effect on geriatric parameters such as Fragility indices and the risk of falls, especially at home. These characteristics are decisive because they define the level of autonomy.

The investigators therefore wish to study the effect of a 2-week treatment with tDCS (tDCS active) versus placebo (2-week tDCS group) on these criteria. This effect may stop or curb cognitive decline.

Inclusion Criteria:

• A man or woman with probable Alzheimer's disease diagnosed according to the criteria of the National Institute of Neurological and Communicative Disorders Association (NINCDS-ADRDA)
• Age ≥ 60 years
• Mini Mental State Examination ≥ 18
• Clinical Demential Rating ≤ 1
• Availability of a caregiver for assessments
• Patient care in Day Hospital
• Informed consent of the subject or his legal representative
• General somatic state consistent with study procedures

Exclusion Criteria:

• Presentation of contraindications to tDCS (presence of intracranial metal implants, intracranial hypertension, comitial risk).
• In case of anticholinesterase treatment: taken for at least 6 months and at a non stable dose for 4 months.
• Taking an antagonist treatment of NMDA receptors (anodic and cathodic) which cancels post-stimulation effects (memantine).
• Other types of dementia or neurological disorder according to Diagnostic and Statistical Manual of Mental Disorders-5 (dementia with Lewy bodies, frontotemporal dementia, Parkinson's disease, Huntington's disease, stroke, major head trauma, cerebral neoplasia, systemic disease ...) , Which can lead to alterations in the functioning of the central nervous system.
• psychiatric disorder according to DSM-5, other than Alzheimer's disease including amnestic disorders, delirium, schizophrenia or schizoaffective disorder, bipolar disorder, major depressive episode in progress, psychosis, panic attacks, post traumatic stress disorder And / or cognitive impairment not otherwise specified.
• Any other disorder for which treatment is given priority over the treatment of Alzheimer's disease or is likely to interfere with the study treatment or impairing adherence.
• Accommodation in an institution (EHPAD, EHPA) or request in progress.
• Participation in other biomedical research during the study that may interfere with the objectives of the study.
• Person who had a recent change (<1 month) of psychotropic treatment.
• Person with a place of residence more than 80 km away.
• Person without health insurance.

the operator enters in the tDCS apparatus the code number of the kind of stimulation to deliver; This code number has been randomly assigned, and the correspondence list is not accessible by the different research professionals.